What is the name of the transformation in which each point on a figure is turned through a given angle and direction around a given point?

The name of transformation is rotation.

Step-by-step explanation:

A rotation is a transformation that turns a figure about a fixed point called the center of rotation.  assume a positive angle of rotation turns the figure counterclockwise, and a negative angle turns the figure clockwise.

Hence, each of the point in the figure also get transformed by the same angle.

Example: Rotate the rectangle ABCD 90° clockwise about the point (0,-1).

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right