Question

a figure is rotated 180 degrees around the origin and then dilated by a scale factor of -2. how will the coordinates of the point (3, -4) change?
a. (6,8)
b. (6, -8)
c. (-6, -8)
d. (-6,8)

what is the result of reflecting a rectangle over the x - axis and then dilating it by a scale factor of 0.75?

Explanation:

Step1: Rotate the point 180 - degrees

The rule for a 180 - degree rotation around the origin is $(x,y)\to(-x,-y)$. For the point $(3, - 4)$, after a 180 - degree rotation, it becomes $(-3,4)$.

Step2: Dilate the rotated point

The rule for dilation with a scale factor $k$ is $(x,y)\to(kx,ky)$. Here $k = - 2$. So, $(-3\times(-2),4\times(-2))=(6,8)$.

Answer:

a. $(6,8)$