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?

okay, i will pick points for triangle abc because they are not listed in the problem. i will also find the corresponding points for triangle a'b'c'.

a: (-1,1) < > a': (3,-2)

b: (2,2) < > b': (6,-1)

c: (1,-1) < > c': (5,-4)

1. the transformation is a translation where the triangle is shifted 4 units to the right and 3 units down. thus, each coordinate is shifted 4 units to the right and 3 units down.

2. if you draw the lines, you will see that they have the same slopes. this is because the change in y over the change in x is the same for each coordinate. if you drew another line through c and c' you will see a line with the same slopes as the other two lines. this line will also have a different y-intercept when compared to the other two lines.