Question

The point (-4,1) is rotated 180 degrees counterclockwise using center (-3,0). What are the coordinates of the image?

(my teacher didn't include an image so im sorry if you were wanting one)

A. (-4, -1)

B. (-5, -2)

C. (-2, -1)

D. (4, -1)

Answer 1

I believe the answer is C also trying using the website desmos it helps a lot with graphing

Answer 2

C. (-2, -1)

Explanation:

It can help to plot the points.

For rotation 180 degrees, the center of rotation is the midpoint of the segment joining the given point and its image. That means you want to find the other end of a segment with one end (-4, 1) and midpoint (-3, 0).

For center of rotation O, this means ...

O = (A +A')/2

2O -A = A'

A' = 2(-3, 0) -(-4, 1) = (-6+4, 0 -1) = (-2, -1)

The coordinates of the image are (-2, -1).