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 Topic: point
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A point on a line 2020-01-25
From Samved:
The line 3x/5 - 2y/3 + 1 = 0 contains the point (m, 2m-1). Calculate the value of 'm'.
(3d) Whether line segment intersects triangle 2019-04-13
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.

The point-slope equation for a line 2018-09-23
From Sally:
The equation of the line in point-slope form for the line passing through the point ( 4, -6) and parallel to the line y = -6x + 2. Describe the steps.
A locus of points 2018-09-03
From Ericka:
Find the locus of points three times as far from (0,4) as from (2,0)
The intersection of a curve and a line 2018-03-08
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
The product of the coordinates of a point on a line 2018-01-17
From Sophia:
For any point on line l, the product of the x-coordinate and the y-coordinate is less than or equal to zero , what is the answer?
The distance between the origin and a moving point on a graph 2017-10-16
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
Why does 10x10x10 give 1,000.0000000000001? 2017-04-12
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
Can you construct a regular 21-gon? 2016-03-08
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

A metal gate 2016-02-06
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.
The midpoints of the sides of a quadrilateral 2016-02-05
From Andrea:
The segments, joining, in order the midpoints of consecutive sides of a quadrilateral form a parallelogram.
An 8 pointed star inscribed in a circle 2015-04-10
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.
A tangent to y=x^3 passes through (0,2) 2015-04-05
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
A circle through 3 points 2014-12-04
From priyanka:
Find the equation of a circle passing through the origin and intercept on axes are a and b.
Three collinear points 2014-08-28
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
A circle through three points 2014-02-22
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.
Distance from a point to a line 2013-12-28
From Sue:
I need to find the distances from the west line on 1st Take Point and 2nd Take Point.
Thanks,
Sue

Inflection Point 2013-11-15
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.

Intersection points and diagonals 2013-09-11
From Kenneth:
I was wondering, is there a relationship between the number of sides of a regular n-gon 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.

Percent and percentage point 2013-07-19
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?

I thank you for your assistance.

Points of intersection 2013-05-02
From Bianca:
Find the sets of values of k for which the line y=kx-4 intersects the curve y=x^2-2x at two distinct points.
Is a line lying in a plane an open or a closed region? 2013-02-13
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?
A 5 pointed star in a circle 2012-08-05
From wiljohn:
find the area of a 5 pointed star in the circle with a radius of 12.517
Points per quarter 2012-05-14
From debbie:
A basketball team scores 216 points in 8 quarters . Find the teams point per quarters rate
Simplify the expression 2012-02-12
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)= (t-6)^4 * (t+1)^2
t'= 4(t-6)^3*(1)*(t+1)^2+ 2(t+1)(1)*(t-6)^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.

Two circles 2012-02-08
From crisfe:
find the point where the common cord of the circles x2+y2=25, x2+y2-12x-6y+35=0 process there line centers. what point they intercepts?
Two line segments in the plane 2011-08-15
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.

A point on a circle 2011-08-02
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)?
Points on a graph 2011-02-15
From Maggie:
Which set of ordered pairs can be used to graph y = -2x-1.

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?

A tangent line 2011-01-03
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=-6x-6
(B) y= -3x+1
(C) y= 2x+10
(D) y=3x-1
(E) y=4x+1

Determine if a point is inside a cube 2010-11-24
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((x-xp)+(y-yp)+(z-zp))<=radios if u please could help me
3 equidistant points on a circle 2010-06-21
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.

The minimum point of a quadratic 2009-12-31
From rachel:
y=0.0008x^2-0.384x
What is the minimum point of this equation?

A linear equation 2009-10-22
From Ryan:
How do you convert the equation 2x-6y=7? This is on my homework and I am really stuck!!!
A parabolic bridge 2009-10-03
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
*y-k=(-1/4)(x-h)^2
b) find the highest point of the arch

The midpoints of two sides of a triangle 2009-03-17
From Manis:
Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it.
A line in slope intercept form 2008-12-08
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
3 equidistant points 2008-12-01
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?
The midpoint o a line segment 2008-11-15
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.
A circle tangent to a line and with its centre on another line 2008-11-01
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.
The standard form Ax+By=C 2008-09-26
From Susan:
I am having difficulty changing the point-slope form of the equation of the line y-y1=m(x-x1) 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.
A line through two points 2008-09-10
From Conor:
Find the equation of the straight line which passes through the points (-2,14) and (8,-1)
A tangent to a curve through a point not on the curve 2008-07-23
From Carter:
How does one find the tangent points on a curve, given only the curve's function and the x-intercept 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.

The midpoints of the sides of a quadrilateral 2008-07-22
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]
A point on a graph 2008-07-08
From Rita:
If (2, b) is a point on the graph of y = (x^2) + 4x, find the value of b.
Points on a graph 2008-07-03
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)

The area of a 5-point star 2008-06-27
From rebecca:
Hello, For a maths extension program i've been given the challenge of finding the area of a 5-point 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
The shortest distance from a point to a line 2008-04-03
From Katherine:
How do I find the shortest distance from the point (3,5) to the line x = -2
The equation of a line 2008-02-17
From Jennifer:
Given the point A(3,2)B(5,8) find the equation of the line AB ( in standard form )
The slope intercept form of a line 2008-02-17
From chris:
find the slope and y intercept of the line (2x+4)-3y=11(x-1) is this equation in slope point form.
Inflection points 2008-01-25
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 2008-01-15
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?
Smallest cone containing a 4cm radius inscribed sphere 2007-12-19
From Eva:
A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone.
Find the radius of a circle given the center and a point on the circle 2007-11-18
From Raymund:
Find the radius if the center is at (0, -5) and one point on the circle is (2,3)
Local maxima, minima and inflection points 2007-11-13
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

Find the equation of a line given two points 2007-10-05
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.
Points that are 15 units from the origin 2007-09-20
From Paula:
Find the coordinates of any point(s) 15 units away from the origin with an x-coordinate 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!

Point-slope form 2007-08-16
From jenny:
write an equation in the point-slope 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)
Slopes of a triangle's medians 2007-08-11
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)
Points in a plane 2007-06-01
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 2007-04-04
From Lenny:
What is a set of points in space the same given distance from its center point called?
Area of a five-pointed star 2007-03-05
From Ashley:
What is the area of a five pointed star inscribed in a circle with a radius of 10cm?
Maximizing profit 2007-01-23
From Denise:
Total Profit= Total Revenue-Total 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
Points of intersection 2007-01-18
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 2006-08-20
From Gianella:

Find the points of intersection by solving this problem analytically.

y= x cubed
y= x

Find the points of intersection 2006-08-18
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

What's the difference between percentages and points? 2006-04-21
From Sayed:
What is the difference between percentages and points?
Equation of a line in Ax + By = C form 2006-04-19
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?
Find the point of inflexion for the curve y = e^x/(x^2-1) 2006-03-31
From Sam:
Hi, i am trying to find the point of inflexion for the curve y = ex/(x2-1) and i got a really complex expression for y". I can't seem to solve x4-4x3+4x2+4x+3=0 so does that mean there is no point of inflexion?
The centroid of a triangle 2006-01-18
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!
y - y1 = m(x - x1) 2006-01-08
From Greg:
How do you change 2x + 3y = 7 into y - y1 = m(x-x1)?
A point is twice the distance from y = 5 + 2x as it is from y = 5 - 2x 2005-12-09
From Hazel:
A point moves so that its distance from the line y=5+2x is twice its distance from the line y=5-2x. Find the general form of the equation of its locus.
What shape do I say a football is? 2005-11-14
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?
Equidistant from the points (2,-1,1) and (0,1,3) 2005-11-06
From Roy:

Find the point on the y-axis that is equidistant from the points (2,-1,1) and (0,1,3).

Find the point not on the y-axis 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 2005-03-30
From carly:
Find the shortest distance from the point (-15, 2.5) to the line 5x+6y=30.
The tangent line at an inflection point 2004-11-28
From Louise:
the equation of the tangent line to the curve y = x3 - 6x2 at its point of inflection is...
A fixed point problem 2004-11-14
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.
The point slope form of a line 2004-10-26
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
A rate of change problem 2004-10-15
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.
Intersecting a line and a curve 2004-01-29
From Senthil:
between line and curve how can i find intersection point? could you write me the formula and explanation also sir.
A point and a line 2003-11-19
From Meenakshi:

Given a line segment L(x1,y1) to (x2,y2) and a Point P(x3,y3).
I need the formula to find a point on the line L that is closest to the point (x3,y3).

The sketch of a graph 2003-10-07
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)x3-2x2+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.
The mean house price 2003-09-10
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.

Collinear Points 2003-01-13
From Gary:

Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?

1. P(1), the point where the angle bisectors intersect.
2. P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
3. P(3), the point where the medians intersect.
4. P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.

This is for my 9-12 high school class in geometry.
My name is Gary

Gary

Answered by Harley Weston and Chris Fisher.
Compass points 2002-11-05
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.
A set of points in space 2002-03-18
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).

Prove that the medians of triangle PQR meet in a central point G. 2001-11-11
From Jessica:
Use a scalene triancle with one point (0,b) on the y axis, another point (2c, 0) on the x-axis and the last point, (2a,0) on the x-axis. Prove that the medians of triangle PQR meet in a central point G.
A 3 dimensional 5 pointed star 2001-11-08
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!
The shortest distance from a point to a line 2001-06-05
From Kat:
Find the shortest distance from the given line. Round to the nearest tenth. (-2,-1) and x+5y+20=0
A point that a group of lines pass through 2000-12-05
From Ross:
A point that a group of lines pass through is called a________?
Midpoints and endpoints 2000-02-15
From Jessica Sipes:
I need to know how to find and endpoint using the midpoint and the other endpoint.
Parabolic mirrors 1999-11-07
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?

Graph question 1998-05-12
From Rose Seminary:
Why is the point of intersection of two lines the solution to the corresponding system of equations?
How many intersections? 1997-10-08
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?

Problème avec rapport point, prix... 2005-09-08
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.