







A point on a line 
20200125 

From Samved: The line 3x/5  2y/3 + 1 = 0 contains the point (m, 2m1). Calculate the value of 'm'. Answered by Penny Nom. 





(3d) Whether line segment intersects triangle 
20190413 

From rj: Well hello,
Lets say I have a triangle,
Not any ordinary triangle, but a triangle that is represented in 3 dimensions. I also have a line segment.
Lets say that this triangle has points A(0,0,0), B(1,0,0), C(0,1,1)
And the line segment has points D(0,1/2,0), E(1,1/2,1)
In what way can I find if the line segment and triangle intersect? Their intersection point?
I don't prefer matrices, because they don't make any sense, but ... if that's the only way to solve this, then do what's necessary.
Thank you in advance. Answered by Penny Nom. 





The pointslope equation for a line 
20180923 

From Sally: The equation of the line in pointslope form for the line passing through the point ( 4, 6) and parallel to the line y = 6x + 2. Describe the steps. Answered by Penny Nom. 





A locus of points 
20180903 

From Ericka: Find the locus of points three times as far from (0,4) as from (2,0) Answered by Penny Nom. 





The intersection of a curve and a line 
20180308 

From lola: find the set of values of constant C for which the line y=x+c intersects the curve y=2 square root x at, at two distinct points Answered by Penny Nom. 





The product of the coordinates of a point on a line 
20180117 

From Sophia: For any point on line l, the product of the xcoordinate and the ycoordinate is less than or equal to zero , what is the answer? Answered by Penny Nom. 





The distance between the origin and a moving point on a graph 
20171016 

From Paulina: Find the rate of change of the distance between the origin and a moving point on the graph of y=x^2 +1 if dx/dt=2 centimeters per second Answered by Penny Nom. 





Why does 10x10x10 give 1,000.0000000000001? 
20170412 

From Randolph: Hi, On your calculator I found that a box 10 by 10 by 10 inches has a volume of 1,000.0000000000001 cubic inches. Can you explain the numeral 1 thirteen places past the decimal? Thanks, Randy Answered by Penny Nom. 





Can you construct a regular 21gon? 
20160308 

From Peter: hi, i know that if i use a compass to draw a circle, i can use the same setting to mark 6 intervals along the circle circumference, how would i go about marking out 21 equally spaced points around the circumference?
if there an online calculator i can us, or some other interesting trick?
tia
peter Answered by Robert Dawson. 





A metal gate 
20160206 

From Carl: I am a welder and I build gates. I have to put holes in a rail and then bend the rail
in a curve. The problem is that the holes in the curved rail must line up with holes
in the other straight rails. How do I calculate where to put the holes in the rail
before I bend it? I will send a drawing if necessary. Answered by Harley Weston. 





The midpoints of the sides of a quadrilateral 
20160205 

From Andrea: The segments, joining, in order the midpoints of consecutive sides of a quadrilateral form a parallelogram. Answered by Penny Nom. 





An 8 pointed star inscribed in a circle 
20150410 

From Kermit: How do you find the area of the star that is formed by two squares and surrounded by a circle. The only given information is that the radius of the circle is 10. Answered by Penny Nom. 





A tangent to y=x^3 passes through (0,2) 
20150405 

From Kevin: Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line Answered by Penny Nom. 





A circle through 3 points 
20141204 

From priyanka: Find the equation of a circle passing through the origin and intercept on axes are a and b. Answered by Penny Nom. 





Three collinear points 
20140828 

From jhanavi: p,q,r are three collinear points.p and q are(3,4) and (7,7) respectively and PR is equal to 10 units.find coordinates of R Answered by Penny Nom. 





A circle through three points 
20140222 

From Mohammad: Find the equation of circle passing through the origin and the points (a,b) and (b,a).
Find the length of chords that it cuts off from the axes. Answered by Chris Fisher. 





Distance from a point to a line 
20131228 

From Sue: I need to find the distances from the west line on 1st Take Point and 2nd
Take Point.
Thanks,
Sue Answered by Penny Nom. 





Inflection Point 
20131115 

From Z.: I was wondering if the function F(x)= x/ln(x) had an inflection point?
If yes, why it's not visible on the graph of the function?
Thanks. Answered by Penny Nom. 





Intersection points and diagonals 
20130911 

From Kenneth: I was wondering, is there a relationship between the number of sides of a regular ngon and the number of times its diagonals intersect?
Ie:
4 sides=1 intersect (center, diagonals form an 'X' )
5 sides=5 intersects (diagonals form a star)
6 sides=13 intersects
And so on. Answered by Chris Fisher. 





Percent and percentage point 
20130719 

From Kenneth: Hello:
Does 0.01 represent both one percentage point and one percent in decimal form?
What is, for example, 2/100 of one percentage point, and what is 2/100 of one percent?
Are the answers the same.
I thank you for your assistance. Answered by Penny Nom. 





Points of intersection 
20130502 

From Bianca: Find the sets of values of k for which the line y=kx4 intersects the curve y=x^22x at two distinct points. Answered by Penny Nom. 





Is a line lying in a plane an open or a closed region? 
20130213 

From pardeep: please help with this question on the open and closed intervals ::
Is a line lying in a plane an open or a closed region? my teacher says it is a closed region reasoning out that it contains all it boundary points. please help how is it so? Answered by Harley Weston. 





A 5 pointed star in a circle 
20120805 

From wiljohn: find the area of a 5 pointed star in the circle with a radius of 12.517 Answered by Chris Fisher. 





Points per quarter 
20120514 

From debbie: A basketball team scores 216 points in 8 quarters . Find the teams point per quarters rate Answered by Penny Nom. 





Simplify the expression 
20120212 

From Christy: Hi guys, ok so I'm having problems with solving this equation since it's been so long I've done precal.
I have to find critical points so I have to find the derivative first. This is what I've done so far
s(t)= (t6)^4 * (t+1)^2
t'= 4(t6)^3*(1)*(t+1)^2+ 2(t+1)(1)*(t6)^4
so this is where I got stuck, which is the algebra part. How can I simplify this to get the answer to figure out the critical points. Answered by Penny Nom. 





Two circles 
20120208 

From crisfe: find the point where the common cord of the circles x2+y2=25, x2+y212x6y+35=0 process there line centers. what point they intercepts? Answered by Penny Nom. 





Two line segments in the plane 
20110815 

From Tim: For this problem I actually have tried to visualise the image in my head many times. This question makes my head spin.
Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value.
Prove that these segments have no common points. Answered by Chris Fisher. 





A point on a circle 
20110802 

From George: I know the center location (x,y) of the circle, I know the radius of the circle, I know the location (X,Y) of one point on the circle, and I know the angle (in degrees not radians) between the known point location (X,Y) and an unknown point location (let's call it (A,B) for reference). What formula(s) can I use to find out the coordinate position of (A,B)? Answered by Chris Fisher. 





Points on a graph 
20110215 

From Maggie: Which set of ordered pairs can be used to graph y = 2x1.
A.(5,9),(1,3),(4,9) B. (2,5),(1,1),(5,9)
C.(2,5),(0,1),(4,3) D. (5,9),(2,3),(4,9)
I cannot figure it out. Could you help me? Answered by Penny Nom. 





A tangent line 
20110103 

From Amanda:
Question from Amanda, a student:
an equation of the line tangent to y=x^3+3x^2+2 at its point of inflection is
(A) y=6x6
(B) y= 3x+1
(C) y= 2x+10
(D) y=3x1
(E) y=4x+1 Answered by Penny Nom. 





Determine if a point is inside a cube 
20101124 

From Ali: hi every one
i have a problem with cube
they told me to write a program that determine if a point is
inside a cube
so i need the equation of the cube to do the comparison.
in sphere it is easy
sqrt((xxp)+(yyp)+(zzp))<=radios
if u please could help me Answered by Robert Dawson. 





3 equidistant points on a circle 
20100621 

From Brian: We have to line up 3 pins on a lifting bridle to be 120 degrees apart from each other to connect into a lifting assembly.
I know pi*d. I know straight lines connecting these points to each other will result in an equilateral triangle.
How does one find these points without using a protractor? There must be a formula (formulae) to work this out mathematically.
r = 10.5 inches
pi*d = 65.9736
3 segments( arcs) = 21.9912 which is the distance along the circumference that the points are from each other. Answered by Penny Nom. 





The minimum point of a quadratic 
20091231 

From rachel: y=0.0008x^20.384x
What is the minimum point of this equation? Answered by Penny Nom. 





A linear equation 
20091022 

From Ryan: How do you convert the equation 2x6y=7? This is on my homework and I am really stuck!!! Answered by Penny Nom. 





A parabolic bridge 
20091003 

From SANDRA: a bridge is constructed across the river that is 200 feet wide. the arch is parabolic
so that the focus is on the water. A sheep 50 ft wide and 30 ft high passes safely
through the arch
a) find equation of the arch
*yk=(1/4)(xh)^2
b) find the highest point of the arch Answered by Stephen La Rocque. 





The midpoints of two sides of a triangle 
20090317 

From Manis: Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it. Answered by Robert Dawson. 





A line in slope intercept form 
20081208 

From laurie: the question: Write and equation of the line that passes through the point
and has the give slope. Then rewrite the equation in slope intercept form.
(2, 5 ) m= 3 Answered by Penny Nom. 





3 equidistant points 
20081201 

From Damien: How do you find 3 equidistant points (C,D,E) on a line between point A(Xa, Ya) and point B(Xb, Yb) so that AC, CD, DE and EB are all equal? Answered by Chris Fisher. 





The midpoint o a line segment 
20081115 

From Jane: The vertices of a triangle are at (1,7), (6,1) and (0,3). Find the coordinates of the midpoints of the sides. Answered by Penny Nom. 





A circle tangent to a line and with its centre on another line 
20081101 

From liza: Find the equation of the circle of radius squareroot 26 tangent to the line 5x+y=13 and having its center on the line 3x+y+7=0. Answered by Chris Fisher. 





The standard form Ax+By=C 
20080926 

From Susan: I am having difficulty changing the pointslope form of the equation of the line yy1=m(xx1) to the standard form Ax+By=C. You must express A,B,C in terms of the constants m,x1,y1. I have been able to insert numbers and switch easily from the general to the point slope equation, but I am stumped on how to convert it this way. Answered by Penny Nom. 





A line through two points 
20080910 

From Conor: Find the equation of the straight line which passes through the points (2,14) and (8,1) Answered by Penny Nom. 





A tangent to a curve through a point not on the curve 
20080723 

From Carter: How does one find the tangent points on a curve, given only the curve's function
and the xintercept of that tangent line?
i.e. Find the point(s) on the curve y = (x^2) + 1, where the tangent line passes
through the point (2, 0).
I know that there will be two such points, one where y is very close to 1, and the
other point where y is a large negative number. However, I do not recall how to
figure out the tangent line equation given a single intercept and solving to find the
tangent points. Answered by Penny Nom. 





The midpoints of the sides of a quadrilateral 
20080722 

From JOEL: A QUADRILATERAL A,B,C,D HAS THE CO ORDINATE [2,5],[8,7],[10,3]&[0,1] RESPECTIVLY [B,E,G,H] ARE THE MID POINTS OF THE SIDES AB,BC,CD&DA RESPECTIVLY FIND THE MID POINTS OF [FG]&[FH] Answered by Penny Nom. 





A point on a graph 
20080708 

From Rita: If (2, b) is a point on the graph of y = (x^2) + 4x, find the value of b. Answered by Leeanne Boehm. 





Points on a graph 
20080703 

From Rita: Dertermine if the given 3 points are on the graph of the equation.
Equation: y = (x^3)  [2(sqrt{x})]
Points: (0, 0); (1, 1); (1, 1) Answered by Penny Nom. 





The area of a 5point star 
20080627 

From rebecca: Hello,
For a maths extension program i've been given the challenge of finding the area of a 5point star with each of the 10 outside edges being a length of 1.23cm
How might I go about finding the area for such a shape given only this piece of information?
Sincerely, Rebecca Answered by Janice Cotcher. 





The shortest distance from a point to a line 
20080403 

From Katherine: How do I find the shortest distance from the point (3,5) to the line x = 2 Answered by Stephen La Rocque. 





The equation of a line 
20080217 

From Jennifer: Given the point A(3,2)B(5,8) find the equation of the line AB ( in standard form ) Answered by Penny Nom. 





The slope intercept form of a line 
20080217 

From chris: find the slope and y intercept of the line (2x+4)3y=11(x1)
is this equation in slope point form. Answered by Penny Nom. 





Inflection points 
20080125 

From Armando: Hi, Im trying to write a program that takes an equation ( f(x) = 0 ) and returns a list of the inflexion points in a given interval.
there must be (I think) a mathematical method or algorithm to do this, probably involving the (second) derivate of the function.
However I have not found such a method yet. Any help on this will be much appreciated. Answered by Stephen La Rocque and Harley Weston. 





Maximum volume of a box 
20080115 

From Rajesh: A square piece of a cardboard of sides ten inches has four equal peices are removed at the corners, then the sides are turned up to form an open box. What is the maximum volume such a box can have? Answered by Stephen La Rocque. 





Smallest cone containing a 4cm radius inscribed sphere 
20071219 

From Eva: A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone. Answered by Stephen La Rocque. 





Find the radius of a circle given the center and a point on the circle 
20071118 

From Raymund: Find the radius if the center is at (0, 5) and one point on the circle is (2,3) Answered by Stephen La Rocque. 





Local maxima, minima and inflection points 
20071113 

From Russell: let f(x) = x^3  3a^2^ x +2a^4 with a parameter a > 1.
Find the coordinates of local minimum and local maximum
Find the coordinates of the inflection points Answered by Harley Weston. 





Find the equation of a line given two points 
20071005 

From Tiffany: The equation for the line through the points (11,2) and (18,12) can be written in the form Ax+By=C.
Find A and B. Answered by Victoria West. 





Points that are 15 units from the origin 
20070920 

From Paula: Find the coordinates of any point(s) 15 units away from the origin with an
xcoordinate of 9.
I was given the answer: (9,12) and (9,12), but I do not understand how these numbers
were calculated. Thank you for your help! Answered by Stephen La Rocque. 





Pointslope form 
20070816 

From jenny: write an equation in the pointslope form and the intercept form
slope=4,passing through (1,3)
slope=8,passing through (4,1)
slope= 5,passing through (4,2)
slope= 2,passing through(0,3) Answered by Leeanne Boehm. 





Slopes of a triangle's medians 
20070811 

From Gina: I am trying to help my daughter with this, but I am very weak in Math.Please help!
Find slopes of the medians of a triangle whose vertices are P(1,3), Q(3,5), and R(6,2) Answered by Stephen La Rocque. 





Points in a plane 
20070601 

From Gabrielle: In general how many planes are there which contain two given points, three given points, and four given points? Answered by Steve La Rocque and Walter Whiteley. 





A set of points in space 
20070404 

From Lenny: What is a set of points in space the same given distance from its center point called? Answered by Stephen La Rocque. 





Area of a fivepointed star 
20070305 

From Ashley: What is the area of a five pointed star inscribed in a circle with a radius of 10cm? Answered by Stephen La Rocque. 





Maximizing profit 
20070123 

From Denise: Total Profit= Total RevenueTotal Cost P(x)=R(x)C(x) Where x is the number of units sold. Find the maximum profit and the number of units that must be sold in order to get that profit. R(x)=5x C(x)=.001x^2+1.2x+60 Answered by Stephen La Rocque. 





Points of intersection 
20070118 

From Mark: Find the points of intersection of the given pair of curves. 2x  3y = 8 and 3x  5y = 13 Answered by Steve La Rocque and Haley Ess. 





Points of intersection 
20060820 

From Gianella:
Find the points of intersection by solving this problem analytically.
y= x cubed
y= x
Answered by Stephen La Rocque. 





Find the points of intersection 
20060818 

From Ingrid:
The question says find the points of intersection of the graphs of the equation, and check your results analytically.
x squared + y squared=25
2x+ y=10
Answered by Stephen La Rocque. 





What's the difference between percentages and points? 
20060421 

From Sayed: What is the difference between percentages and points? Answered by Stephen La Rocque. 





Equation of a line in Ax + By = C form 
20060419 

From Christopher: How do you write the equation of a line with a slope of 3/8 and passing through (4,6) in Ax+By=C form? Answered by Stephen La Rocque. 





Find the point of inflexion for the curve y = e^x/(x^21) 
20060331 

From Sam: Hi, i am trying to find the point of inflexion for the curve y = e^{x}/(x^{2}1) and i got a really complex expression for y". I can't seem to solve x^{4}4x^{3}+4x^{2}+4x+3=0 so does that mean there is no point of inflexion? Answered by Penny Nom. 





The centroid of a triangle 
20060118 

From Andrea: I am trying to find the centriod of a triangle. I have been given the three vertices of the triangle: A (25, 20), B (5, 40), and C (15, 30). I believe I calculated the correct midpoints: AB(E) (5, 5), BC(D) (5, 5), and AC(F) (15, 30). When I graphed these points I came up with the solution (5, 10), but I can't seem to write the answer out (equations of the lines, etc) correctly. Any help would be greatly appreciated! Answered by Penny Nom. 





y  y1 = m(x  x1) 
20060108 

From Greg: How do you change 2x + 3y = 7 into y  y1 = m(xx1)?
Answered by Penny Nom. 





A point is twice the distance from y = 5 + 2x as it is from y = 5  2x 
20051209 

From Hazel: A point moves so that its distance from the line y=5+2x is twice its distance from the line y=52x. Find the general form of the equation of its locus. Answered by Penny Nom. 





What shape do I say a football is? 
20051114 

From Peter: I am a 43 year old man. I am no longer in school, I have a bachelors degree. I like to tell stories about sports in ways to make people think about the amount of time they devote to the sports. For example, while attending a church in Chicago on the north side, I would pass by Wrigley field.
I began to call it the church of the flying orb or sphere. Now if I want to tell a similar story about football (not soccer), what shape do I say a football is? Answered by Chris Fisher. 





Equidistant from the points (2,1,1) and (0,1,3) 
20051106 

From Roy:
Find the point on the yaxis that is equidistant from the points (2,1,1) and (0,1,3).
Find the point not on the yaxis that is equidistant from the points (2,1,1) and (0,1,3).
Answered by Penny Nom and Walter Whiteley. 





The shortest distance from a point to a line 
20050330 

From carly: Find the shortest distance from the point (15, 2.5) to the line 5x+6y=30. Answered by Penny Nom. 





The tangent line at an inflection point 
20041128 

From Louise: the equation of the tangent line to the curve y = x^{3}  6x^{2} at its point of inflection is... Answered by Penny Nom. 





A fixed point problem 
20041114 

From Bob: I am trying to solve an existence of fixed point problem. I need to show that a function f (on reals) with f'(x)=>2 has a fixed
point. Answered by Claude Tardif. 





The point slope form of a line 
20041026 

From Jack: Given a set of ordered pairs, ie (1,1) (2,4) (3,7), how does one determine the rule f(n) other than by trial and error Answered by Penny Nom. 





A rate of change problem 
20041015 

From Frank: Find the rate of change of the distance between the origin and a moving point on the graph of y = x(squared) + 1 if dx/dt = 2 centimeters per second. Answered by Penny Nom. 





Intersecting a line and a curve 
20040129 

From Senthil: between line and curve how can i
find intersection point?
could you write me the formula and explanation also sir. Answered by Penny Nom. 





A point and a line 
20031119 

From Meenakshi:
Given a line segment L(x_{1},y_{1})
to (x_{2},y_{2}) and a Point P(x_{3},y_{3}).
I need the formula to find a point on the line L that is closest to
the point (x_{3},y_{3}). Answered by Penny Nom. 





The sketch of a graph 
20031007 

From A student: I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x^{3}2x^{2}+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer. Answered by Penny Nom. 





The mean house price 
20030910 

From Carol:
Question: I have to find the mean from the following example: Price Range £000  No of Houses  55 and under 60  3  60 and under 65  6  65 and under 70  13  70 and under 80  21  80 and under 100  15  100 and under 130  7  130 upwards  1  I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated. Answered by Penny Nom. 





Collinear Points 
20030113 

From Gary:
Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?  P(1), the point where the angle bisectors intersect.
 P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
 P(3), the point where the medians intersect.
 P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.
This is for my 912 high school class in geometry. My name is Gary Thanks for your help. Gary
Answered by Harley Weston and Chris Fisher. 





Compass points 
20021105 

From Mhairi: I was asked this in maths but I am not sure if it is geography. Name all the compass points? We have been given 8 but he told us there is more and we have to name them. Answered by Chris Fisher. 





A set of points in space 
20020318 

From Victoria: Describe the given set with a single equation or a pair of equations: The set of points in space that lie 2 units from the point(0,0,1) and at the same time 2 units from the point (0,0,1). Answered by Penny Nom. 





Prove that the medians of triangle PQR meet in a central point G. 
20011111 

From Jessica: Use a scalene triancle with one point (0,b) on the y axis, another point (2c, 0) on the xaxis and the last point, (2a,0) on the xaxis. Prove that the medians of triangle PQR meet in a central point G. Answered by Penny Nom. 





A 3 dimensional 5 pointed star 
20011108 

From Kent: I am looking for a formula that will give me a layout for a 3 dimensional 5 pointed star. I want to form it out of sheet metal, using 5 polygons and soldering them at the apex. Can you please help me with this? I would like to be able to give the formula the height of the star from the bottom two points to the top point and also how deep the star is. Thank you very much! Answered by Judi McDonald. 





The shortest distance from a point to a line 
20010605 

From Kat: Find the shortest distance from the given line. Round to the nearest tenth. (2,1) and x+5y+20=0 Answered by Penny Nom. 





A point that a group of lines pass through 
20001205 

From Ross: A point that a group of lines pass through is called a________? Answered by Chris Fisher. 





Midpoints and endpoints 
20000215 

From Jessica Sipes: I need to know how to find and endpoint using the midpoint and the other endpoint. Answered by Penny Nom. 





Parabolic mirrors 
19991107 

From Andy White: I am working on a project concerning parabolic mirrors. I need to create a mirror to focus sunlight on a focal point, but I don't know how to do it. Is there some equation that tells where a focal point will be in relation to a parabola? What is a directrix? Answered by Penny Nom. 





Graph question 
19980512 

From Rose Seminary: Why is the point of intersection of two lines the solution to the corresponding system of equations? Answered by Penny Nom. 





How many intersections? 
19971008 

From James: (a) A collection of eight points, no three collinear. If lines are drawn between each pair of these points, how many points of intersection would there be? (b) what would your answer have been in part (a) if there had been n points to start with? Answered by Chris Fisher. 





Problème avec rapport point, prix... 
20050908 

From Nico:
Le prix d'un diamant est proportionnel au carré de son poinds. Un diamant de 0.45 g vaut 7500euros.
1. Combie coute un diamant de 0.693 g ?
2. Quel est le poids d'une diamant valant 45000 euros ?
Je vous demande pas de le raisoudre à ma place mais j'aimeré comprendre comment je peut calculé le rapport entre le point et le prix.
Answered by Claude Tardif. 





Point de partage 
20000221 

From Sebastian Murciano: J'aurais besoin de savoir où je peux trouver de l'informations, ou estce que vous pouvez me donner de l'information sur : Point de partage d'un segment étudié en Secondaire 4. Answered by Claude Tardif. 

