







(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. 





A line cuts a curve 
20181111 

From roxanne: Hello, i need to ask a question, do you mind explaining and writing the formula of how to solve equations such as "find the set values of k for which the line y2x5 cuts the curve y=x^2 +kx+11" please Answered by Penny Nom. 





Two curves 
20180923 

From Megan: How do i find the interception points of xy=2 and y=x+3? Many thanks! Answered by Penny Nom. 





Two intersecting tubes 
20180815 

From Tommy: Hi, I am trying to determine a mathematical model for two metal tubes joining at various degrees for weld.
For instance, if I am trying to join the end of a tube to the side of another at a 90 degree angle, it will be a simple profile cut out of the joining tube.
Where it gets tricky is if you want to join the new tube at a given angle.
It would be very helpful if you could give insight as to how I can solve this problem or an equation I could work off of.
Thanks for the help!! Answered by Edward Doolittle. 





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. 





Two circles 
20170813 

From Ladines: Find the equation of the circle passing through points of intersections of circles x²+y²=4y and x²+y²=2x and the center is on line y=2 Answered by Penny Nom. 





Two wires between two buildings 
20170511 

From Bill: I need to find the height of the intersection point of two building wires< br />
Building A is 860 feet high and building B is 480 feet high. The wires existent from the top of one building to
The bottom of the other < br />
The distance between is 32 feet Answered by Penny Nom. 





The line of intersection of two planes 
20151209 

From Rabz: Determine the vector equation for the intersection between the two given planes
2x+7y equal to 14,x+z equal to 7 Answered by Penny Nom. 





The intersection of a plane and a cone 
20150516 

From Tom: Is there a way to derive an equation that describes the perimeter of the intersection of a plane and a cone regardless of the angle of the plane to the cone. Assume that the plane does not cut through the base of the cone, the x, y, z location of the vertex is known, the distance from the vertex to the plane through the axis is know., and that the angle of the cone is known. Answered by Chris Fisher. 





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. 





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. 





A family of circles 
20110301 

From steffi: Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 4x28=0 and x^2 +y^2 4x20+52=0; the member tangent to x=7. Answered by Penny Nom. 





Intersecting polygons 
20101117 

From Laura: How can I estimate the amount of intersection (area or better a normalized number) between two polygons if I have the cartesian coordinates of their vertices?
Thank you in advance,
regards,
Laura Answered by Robert Dawson. 





Find the point of contact of the circles 
20100920 

From Sandra: If the center of circle A = (1,3) and the radius of it is √20,
the center of circle B = (5,9) and the radius of it is √80.
Find the point of contact of the circles A and B. Answered by Janice Cotcher. 





The intersection of two graphs 
20100627 

From Austin: In depth explanation of how to find the intersection points of functions y=4t+300 and y=4.9(t5)^2+300 Answered by Stephen La Rocque. 





The angle of intersection between two lines 
20100325 

From Madhumitha: How to find the angle of intersection between a line x=249 and another line which is of the form y=m*x+c; Line1 has a slope of infinity so what does the angle of intersection turn out to be? Or how can i find it? Answered by Chris Fisher. 





Prove A intersect B =X iff A = X and B = X 
20100306 

From Gloria: how would you prove A intersect B =X iff A = X and B = X Answered by Tyler Wood. 





The acute angle formed by intersecting lines 
20091217 

From Katie: To the nearest tenth of a degree, find the size of the acute angle formed by the intersecting lines 3x + 2y = 12 and x  2y = 2. Was is necessary to find the intersection point? Answered by Robert Dawson. 





The point of intersection of the pair of straight lines 
20091119 

From Stephanie: Find the point of intersection of the pair of straight lines:
y=3x9
y=4x+2
x = _______ and y = ________
I am totally confused. Please help Answered by Robert Dawson. 





The intersection of two graphs 
20091030 

From asma: by using the suitable scales,draw both the graph of x/2 + y/4 =3 and y=2 on the same graph paper.Find the points of intersection of the two graph. Answered by Penny Nom. 





The intersection of two graphs 
20090902 

From Jaqueline: Find the points of intersection of the graphs of the equations
x^(2 )+ y^2=25 and 2x + y = 10 Answered by Penny Nom. 





Intersection of Two Curves 
20090727 

From Amarah: Find the coordinates of the point A( this point is where the two lines intersect). Justify answer
question : here is a curve x^y =y^x (for x,y>o) Answered by Janice Cotcher. 





Finding the Line Joining Perpendicular Feet 
20090716 

From mukulu: Please help I've been tryng to search in your data but i failed to get the solution Find the equation of a straight line joining the feet of the perpendiculars drawn from the point A(1,1) to the line 3x3y4= 0 and 3x+y6=0. Answered by Janice Cotcher. 





The intersection of two lines 
20090130 

From kaylee: how do you find and graph the intersect of these two equations:
y=2x4 (and) 2y=x
thanks,
kaylee Answered by Stephen La Rocque. 





The point of intersection of the straight lines 
20090118 

From Kieran: Find the point of intersection of the straight lines
y=2x+4, and y+2x16=0 Answered by Robert Dawson and Penny Nom. 





(a x b) intersect (b x a) 
20090108 

From sean: is it possible to have two sets such that
n((a X b) intersect (b X a) =3 Answered by Harley Weston. 





A union B and A intersect B 
20090107 

From Jim: Suppose A and B are sets and (A union B) = (A intersect B). Is it true that A=B. Answered by Penny Nom. 





The empty set 
20080929 

From wahab: Why a null set is called a set?
the definition of set includes that a set is a collection of well defined objects
But a null set is having no value. Answered by Harley Weston. 





The intersection of the medians 
20080818 

From Katie: Q: A Triangle is positioned with one side on the xaxis, the coordinates
for the triangle are (a,0), (a,0), (b,c)
a) Find the coordinates of the point of intersection of the perpendicular
bisectors of the sides
b) Find the coordinates of the point of intersection of the medians
c) Find the coordinates of the point of intersection of the altitudes Answered by Penny Nom. 





Two intersecting circles 
20080417 

From Muhammad: Hi, how can we find the perimeter and area of the region common to two intersecting circles of radii 6 cm and 4 cm with centers 7 cm apart. Answered by Harley Weston. 





Finding equations, intersection point of two lines at right angles 
20070922 

From Yaz: Find the equation of the line joining A(1,9) to B(6,120). Another line passes through C(7,5) and meets AB at rigth angle of D. Find the euation of CD and calculate the coordinates of D. Answered by Stephen La Rocque. 





The intersection of two planes 
20070531 

From Sarim: How to find a intersection of two planes? Answered by Penny Nom. 





Two lines intersect at a right angle 
20070420 

From ellen: The line with the equation 3x + by = 6 intersects with the line 6y + ax = c at right angles at the point
(4,6). Determine the values of a, b & c. Answered by Stephen La Rocque. 





Intersection of a line and a circle 
20070412 

From gaby: The sum of two numbers is 9. The sum of the squares of the two numbers is 41. Find the numbers. Answered by Steve La Rocque and Melanie Tyrer. 





The intersection of two lines 
20070228 

From Tamara: I was told to make a graph to help solve this question. I was given two equations. One was x2y=3 and the other was 2x+y=4. We have to change it to the equation of the line format. Then we graph the line and find the point where they meet. I've been trying to do that, but when i check the answer, It turns out wrong. It's meeting in the wrong spot. I need help please. Answered by Penny Nom. 





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. 





The intersection of a line and a circle 
20060202 

From Bernice: if i am given an equation of a circle and 2 points in a line how do i know if the line intersects the circle and how do i determine the points of intersection Answered by Chris Fisher. 





Two intersecting lines 
20041218 

From James: Imagine a vertical line 1.107' tall. Leaving the top of this line, sloping down to the right at a 4:1, at what horizontal distance will the line strike a second line, which leaves the the bottom of the vertical line sloping down to the right at a rate of .02 ft/ft (or 2%)? There is a fairly easy solution to this, but I have lost my notes! Answered by Harley Weston. 





The points of intersection of two graphs 
20041105 

From Benjamin: How do I find the points of intersection of the two functions:
1) y = 2  ex
2) y = 1 + x2 Answered by Harley Weston. 





The intersection of planes 
20040907 

From Joshua: I was wondering about the intersection of planes. Can planes intersect? Answered by Penny Nom. 





The intersection of two graphs 
20040728 

From JJ: Is there a way to find the intersections of these graphs algebraically?
x^2 + y = 4 & 2x  y = 1
I got (1.45, 1.9) and (3.45, 7.9) with a graphing calculator.
AND THESE...
y = 3.29x & y = 5.5(x^0.5)+ 10000
I got x at 3133 with a graphing calculator.
Answered by Penny Nom. 





The intersection of two graphs 
20040331 

From Benjanim: How do I find the points of intersection of the two functions:
1) y = 2  (e^x)
2) y = 1 + (x^2)
I know that I have to set them equal to each other, but I can't solve for x. Please help :) 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. 





Squares in a rectangle 
20031021 

From Raj:
Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle. If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares. Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle. Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle? Answered by Chris Fisher. 





Can 2 vertical planes intersect? 
20030906 

From Erin: My question is can 2 vertical planes intersect? Answered by Penny Nom. 





The intersection of conics 
20021219 

From Glenda: We are studying systems of equations where two conic sections are the two equations that we are solving simultaneously. We were studying the number of solutions that are possible if you have an ellipse and a parabola. We all agree that there can be none, one, two, three or four solutions. The question that the students had for me was whether or not a portion of an ellipse and a parabola can overlap and thereby allow an infinite number of solutions. What should I tell them? Answered by Chris Fisher and Harley Weston. 





Diagonals in a polygon 
20020410 

From Murray: If you have a regular polygon with n sides and you draw all (n3)n/2 diagonals how many intersection will they form with each other and how many sections will they devide the polygon into. Answered by Caude Tardif and Chris Fisher. 





If you conect all the vertices of a regular ngon... 
20020401 

From Murray: If you conect all the vertices of a regular ngon with lines you will have (n3)(n/2) lines inside the polygon. I want to find out how many sections these lines divide the polygon into and how many intersections they have with each other. Answered by Claude Tardif. 





Intersection of perpendicular cylindrical surfaces 
20010731 

From Charlie: Please consider two right circular cylinders, perpendicular one to the other, and of unlike radii in a 3 dimensional Cartesian space with mutually perpendicular x,y,z axes. If one cylinder is centered on the y axis with radius ra, and the other on the z axis with radius rb, then the expression for the first surface would be x^{2} + z^{2} = ra^{2}, y = any number. Likewise, the second cylinder's surface would be x^{2} + y^{2} = rb^{2}, z = any number. It is my intent to define the curve at the intersection of these two cylindrical surfaces. From sketching the conditions it appears that this intersection resembles an ellipse folded about its minor axis. Answered by Chris Fisher. 





Where do the lines y=2x4 and y=x1 intesect? 
20010406 

From Bryce: solve the following problem by setting them equal to each other. Solve for x and y. Where do the lines y=2x4 and y=x1 intesect? 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. 





Angle of Intersection of Two Lines 
20000302 

From Veronica Patterson: I am having a real hard time trying to figure out this problem. Could you please help me! The homework question says to find the acute angle of intersection between the two lines y=3x+1 and y=(1/2)x1. (It also says to use the results of a problem I had already figured out.) That problem was to use information from a picture shown that tan(theta sub1theta sub2)= ((m sub2 m sub1)/(1+(m sub1 * m sub2))). I used the difference identity of tangent to figure out the answer. Any help on this problem would be greatly appreciated. Answered by Harley Weston. 





Notation 
19990903 

From Judy Gray: My name is Judy Gray. I guess the level on this would be about middle school, and I am an other!! I've been out of school for alot of years. I have a couple of questions, I guess.  What does an equal (=) with a slash through it mean? I put intersects, but I think I'm wrong.
 What is the symbol of a small n? Only the symbol is wider. Example: If A = {1.2} B = {2,3} then what is A (n) B? Can you make sense out of that?
 What is the equation of the yaxis?
Answered by Penny Nom. 





Dividing a Circle 
19990412 

From Mike Kenedy: I am having trouble with a homework question for bonus marks. A Circle is continually divided by lines that do not intersect the center so that they produce the most pieces of circle. For example  1 line divides the circle into 2.
 2 into 4.
 3, however into 7.
 4 into11
 5 into 16
 6 into 22
 7 into 29
 8 into 37
 etc...
I am stumped and cannot figure out the equation, though I'm sure it involves squares. Can you help? Answered by Penny Nom. 





Intersection of Planes 
19981203 

From Lindsay Fear: My name is Lindsay Fear. I am an OAC student (which is the Ontario equivalent to Grade 12 in most other states and provinces). I am in an Algebra and Geometry course and am currently studying a unit on equations of planes. Our teacher has given us this question that my friend and I have attempted several times, but we are still unable to solve it. My teacher has also suggested using the internet as a resource. The question is: Prove that a necessary condition that the three planes x + ay + bz = 0 ax  y + cz = 0 bx + cy  z = 0 have a line in common is that a^2 + b^2 + c^2 + 2abc = 1 Answered by Walter Whiteley. 





Intersection of planes 
19981122 

From Dave Rasmussen: I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Coordinate Geometry. I have been teaching my students to write equations of planes and lines,  to find the intersection of these and the distance between them. What I am having difficulty finding are good applications of these techniques to "real world" situations. Can anybody help me? Answered by Walter Whiteley and Harley Weston. 





Intersecting Lines. 
19980210 

From Erik Heppler: My typewriter frequently makes mistakes. Suppose I gave you the following system of equations to solve: 35.26X + 14.95Y = 28.35 187.3X + 79.43Y = 83.29 When I looked back, I realized that I meant to use 14.96 as the "Y" coefficient in the first equation instead of 14.95. Solving the system using 14.95 and then solving another system using 14.96 with all other values the same both times results in the intersection points (1776, 4186) and (770, 1816) respectively. How can that be? Answered by Penny nom. 





Calculating the Intersection Point. 
19971210 

From Milton Parsons: Given 2 lines through (x1,y1),(x2,y2),and (x3,y3),(x4,y4). Can you give me a good formula for calculating the intersection point. I would greatly appreciate it.Thanks. Answered by Chris Fisher and 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. 





Where do 2^x and x^2 intersect? 
19960723 

From Darin M Selfridge: The intersecting points of y=2^x and y=x^2, graphed along with x^2=2^x, are obviously three... (2,4), (4,16) and (?,?). I am having problems figuring out the value, and even an equation for the (?,?). Can you help? Answered by Harley Weston Chris Fisher. 

