It says to draw a picture with the 3 points A, B, and C so that AB + BC ≠ AC but that would be super hard to do on here so could you try to explain it? I'm stuck.
If points A, B, and C are not collinear (i.e., in a single straight line), then AB + BC will never equal AC.
If the points are collinear, then AB + BC = AC if and only if B is between A and C. If B is on one of the ends, thus making either A or C the point that's between the other two, then again, AB + BC will never equal AC.
A classic example that illustrates this is a right angle triangle.
Imagine three points (A, B, C) making a right angle triangle with B at the point of the right angle.
If distance from A to B is 3 and distance from B to C is 4 then distance from A to C is 5 and not (3+4).
You can see why that is that case visually if you draw it out. You can calculate distance of A to C which is the long side of the triangle using Pythagoras' Theorem.
Answers & Comments
If points A, B, and C are not collinear (i.e., in a single straight line), then AB + BC will never equal AC.
If the points are collinear, then AB + BC = AC if and only if B is between A and C. If B is on one of the ends, thus making either A or C the point that's between the other two, then again, AB + BC will never equal AC.
A classic example that illustrates this is a right angle triangle.
Imagine three points (A, B, C) making a right angle triangle with B at the point of the right angle.
If distance from A to B is 3 and distance from B to C is 4 then distance from A to C is 5 and not (3+4).
You can see why that is that case visually if you draw it out. You can calculate distance of A to C which is the long side of the triangle using Pythagoras' Theorem.
http://www.mathsisfun.com/pythagoras.html
Draw the points where the angles of a triangle would be.
On a straight line, put C between A and B