A figure is rotated 180° about the origin and then translated 4 units up. Which formula demonstrates the effect on each coordinate value correctly?

Question

A figure is rotated 180° about the origin and then translated 4 units up. Which formula demonstrates the effect on each coordinate value correctly?

Responses

A. (−x−4,−y)

B. (−x+4,−y)

C. (−x,−y−4)(−x,−y+4)

D.(−x, −y+4)

Answer 1

Hi Kristine,

Your question

A figure is rotated 180° about the origin and then translated 4 units up. Which formula demonstrates the effect on each coordinate value correctly?

This problem is a 180 degree rotation followed by a translation of 4 units up.

To determine the values for the new coordinates, first figure out the rotation, then the translation.

When you rotate about the origin by 180, the relationship between (x,y) and (x',y') is (-x, -y)

So if you were at (2,3) when you rotate, you would be at (-2,-3)

Next determine the translation of 4 units up. If you move 4 units up, your x value would stay the same, and your new y value would be y+4.

So combine these two and you get

(-x, -y+4)

A. (−x−4,−y)

B. (−x+4,−y)

C. (−x,−y−4)(−x,−y+4)

D.(−x, −y+4)

Hope this helps.