Question

which image shows line segment a being rotated 90° counterclockwise about point r to create line segment b?

a. w
b. z
c. x
d. y

Explanation:

Step1: Recall rotation properties

A \(90^{\circ}\) counter - clockwise rotation about a point changes the orientation of the line segment. The length of the line segment remains the same.

Step2: Analyze each option

• Option W: The length of segment \(B\) seems to be the same as segment \(A\), and the rotation about point \(R\) (by visual inspection of the angle between \(A\) and \(B\) around \(R\)) is \(90^{\circ}\) counter - clockwise.
• Option X: The angle between \(A\) and \(B\) around \(R\) is not \(90^{\circ}\) (it looks like a \(180^{\circ}\) rotation if we consider the orientation change).
• Option Y: The angle between \(A\) and \(B\) around \(R\) is \(0^{\circ}\) (segments \(A\) and \(B\) are parallel and in the same direction, which is a translation, not a \(90^{\circ}\) rotation).
• Option Z: The length of segment \(B\) relative to segment \(A\) is not maintained (if we assume a proper rotation, the length of the pre - image and image should be equal).

Answer:

A. W