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?

The coordinates of points A,B,C are not given, so I cannot graph the triangle. However, the translation rule given tells us to shift the points 4 units to the right and 3 units down. Apply that rule to each point A,B,C to get A', B', and C' respectively. The entire triangle itself will follow the translation rule as well.

Connecting A to A' forms segment AA'. Do the same for B and B' to get segment BB'. The two segments AA' and BB' are parallel. They both have the same slope. The slope is -3/4 which is directly tied to the translation rule of "down 3, over to the right 4". Basically a rephrasing of "move to the right 4, then down 3".

Recall that slope = rise/run. The rise is the change in vertical direction. The run is the change in horizontal direction.

You should find that segment CC' is also parallel to the other segments mentioned (AA' and BB').

Also, the three segments AA', BB', and CC' have the same length of 5 units. You can use the pythagorean theorem to confirm this.

i think the length is 12 and the width is 17