Question

determine a series of transformations that would map figure h onto figure i.
answer attempt 2 out of 2
a rotation of ( 90 ^ { circ } ) counterclockwise about the origin
followed by a reflection over the x - axis.

Explanation:

Step1: Analyze the rotation

First, consider a \(90^{\circ}\) counter - clockwise rotation about the origin. The rule for a \(90^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\).

Step2: Analyze the reflection

Then, consider a reflection over the \(x\) - axis. The rule for a reflection over the \(x\) - axis is \((x,y)\to(x, - y)\).

Combining these two transformations:
Let's assume a point \((x,y)\) on Figure \(H\). After a \(90^{\circ}\) counter - clockwise rotation, it becomes \((-y,x)\). Then, after a reflection over the \(x\) - axis, it becomes \((-y,-x)\)

Answer:

A rotation of \(90^{\circ}\) counterclockwise about the origin followed by a reflection over the \(x\) - axis.