Question

Graph a triangle ABC and perform a translation of (x + 4, y − 3) to create triangle A′B′C′.


Describe the transformation using words. Make sure you refer to the characteristics and the coordinates.
Draw a line through points A and A′ and through points B and B′. What do you notice about the lines you drew? Do you think you would notice the same characteristics if you drew another line through points C and C′? How do you know?

Answer 1

since it says "a triangle", simply pick three points A, B, and C, and make a triangle with them (to make the calculations easier, stick with small integers)

"perform a translation of (x + 4, y − 3)" this means add 4 to the x-coordinate and subtract 3 from the y-coordinate for all three points A B and C you picked from before. the new points become your A' B' and C' respectively

then, as the problem states, draw a line between A and A', as well as between B and B'. you'll notice something interesting about the slopes of the two lines.