Question

figure i is the result of a transformation on figure h. which transformation would accomplish this?
answer
a rotation 90° counterclockwise about
the origin
a rotation 90° clockwise about the
origin
a translation 5 units to the right and 3
units up
a translation 5 units to the left and 3
units down

Explanation:

Step1: Analyze translation

Translation moves a figure without rotation. But Figure I is rotated compared to Figure H, so translation options (a translation 5 units to the right and 3 units up, a translation 5 units to the left and 3 units down) can be eliminated.

Step2: Analyze rotation

For a point \((x,y)\) rotated \(90^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(-y,x)\). For a \(90^{\circ}\) clockwise rotation about the origin, the rule is \((x,y)\to(y, - x)\). By observing the orientation of Figure H and Figure I (the direction of the vertices), we can see that it is a \(90^{\circ}\) counter - clockwise rotation about the origin.

Answer:

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