Question

Explain how to translate the point (5, 2) with the transformations: D2 and r(180,O). Make sure to explain, in words, how you got your final answer, including where the point was after the first transformation.

Answer 1

The correct answer is (-10, -4).  

Explanation:

D2 is a dilation with scale factor 2.  This means that each coordinate in the point gets multiplied by 2:
(5, 2)→D2 = (5*2, 2*2) = (10, 4).

r(180, O) is a 180° rotation about the origin.  This will negate each coordinate of the point; algebraically, (x, y)→(-x, -y).  This means that

(10, 4)→r(180, O) = (-10, -4).

This is our final answer.

Answer 2

The final point will be at (-10, -4).

To perform these transformations, first you have to dilate it by a factor of 2. That means you multiply it by 2 and you will have (10, 4).

Then, you have to rotate it by 180 degrees around the origin. It will be at (-10, -4).