Question

Triangle A'B'C' is formed from Triangle ABC by the transformation (x, y) -> (x + 2, y - 3). How many pairs of corresponding sides are parallel?

Answer 1

Triangle A'B'C' is congruent to Triangle ABC with three pairs of corresponding sides parallel due to the translation.

Step-by-step explanation:

The transformation (x, y) -> (x + 2, y - 3) is a translation, which shifts every point of Triangle ABC two units to the right and three units down to form Triangle A'B'C'. Since a translation is an example of a rigid motion, it preserves the size and shape of the triangle, thus all corresponding sides remain parallel to their pre-image. Therefore, there are three pairs of corresponding sides that are parallel between Triangle ABC and Triangle A'B'C'.