Question

Two points A (-2,6) and B (-8,4) are given. a) Show that the point B is the mirror image of the point A with respect to the line 3x+y+10=0

Answer 1

In order to show that A and B are the mirror images of each other over line 3x+y+10=0, we need to figure out the slope of the line between A and B and the closest distance between A and the line and B and the line. This should show that the line going through A and B is perpendicular to 3x+y+10=0. The two distances should also be equal to each other.

Answer 2

the line perpendicular to y=-3x-10 is:
y = 1/3x +20/3
Both A and B lie on the line.
The midpoint of AB is (-5,5)
The point where the 2 lines intersect is also (-5,5)

Therefore they are equal distances away from each other

Answer 3

team work :)