Question

unit 4 transformations > lesson 16 transformations unit test
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a. what two transformations were completed to move triangle abc to triangle xyz? include the name of the transformation and by how much. example- it was rotated by 180 degrees and reflected over line x = y
b. are the shapes congruent? how do you know?

Explanation:

Step1: Identify transformation 1

The triangle is rotated 180 degrees about the origin. When rotating a point (x,y) 180 - degrees about the origin, the new point is (-x,-y).

Step2: Identify transformation 2

After rotation, the triangle is translated. The vertical translation is 6 units down (since the y - coordinates of corresponding points have a difference of 6) and 2 units to the right (since the x - coordinates of corresponding points have a difference of 2).

Step3: Determine congruence

Congruent shapes have the same size and shape. Rotation and translation are rigid - motions. Rigid motions preserve the size and shape of a figure. So, the two triangles are congruent.

Answer:

a. Rotated 180 degrees about the origin and translated 6 units down and 2 units to the right.
b. Yes, they are congruent. Because rotation and translation are rigid - motions that preserve size and shape.