Question

congruent rectangles hjkl and hjkl are shown on the coordinate grid below. are these shapes congruent? if so, describe a sequence of transformations on rectangle hjkl that would result in rectangle hjkl. hint: use the \\( \boldsymbol{\sqrt{x}} \\) button to type out math expressions and symbols more easily.

Explanation:

Step1: Check definition of congruence

Two shapes are congruent if they have the same size and shape. By visual inspection, rectangles HJKL and H'J'K'L' appear to have the same dimensions.

Step2: Identify transformation

To map rectangle HJKL to H'J'K'L', we first note that there is a translation. If we consider the coordinates of corresponding vertices, we can see that rectangle HJKL is translated 8 units to the right and 4 units up. There is no rotation or reflection involved in this case.

Answer:

Yes, the shapes are congruent. The sequence of transformations is a translation 8 units to the right and 4 units up.