Question

question
figure p is the result of a transformation on figure o. which transformation would accomplish this?
answer
a translation 7 units to the right and 3 units down
a rotation 90° clockwise about the origin
a rotation 90° counterclockwise about the origin
a translation 7 units to the left and 3 units up

Explanation:

Step1: Analyze translation

Translation moves a figure without rotation. The figure \(P\) is not just moved horizontally/vertically in a simple translation way as in options A and D.

Step2: Analyze rotation

For a rotation of \(90^{\circ}\) clockwise about the origin \((x,y)\to(y, - x)\). For a rotation of \(90^{\circ}\) counter - clockwise about the origin \((x,y)\to(-y,x)\).
If we consider a point \((x,y)\) in Figure \(O\) and check the transformation to Figure \(P\). Let's assume a non - origin related point (for simplicity, take a vertex). If we rotate a point \((x,y)\) of Figure \(O\) \(90^{\circ}\) counter - clockwise about the origin, we can see that the orientation of Figure \(P\) matches the result of a \(90^{\circ}\) counter - clockwise rotation.
If we consider a \(90^{\circ}\) clockwise rotation, the orientation will not match.

Answer:

A rotation \(90^{\circ}\) counterclockwise about the origin.