Question

triangle ( jkl ) is the image of triangle ( jkl ) under a rotation about the origin followed by a reflection across the ( x )-axis. write the rules for the rotation and reflection. rotation: ( (x, y) mapsto (square, square) ) reflection: ( (x, y) mapsto (square, square) )

Explanation:

Step1: Determine the rotation rule

Let's assume the rotation is \(90^{\circ}\) counter - clockwise. The rule for a \(90^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(-y,x)\).
Take a point from \(\triangle JKL\), say \(J(3,1)\). After rotation (assuming \(90^{\circ}\) counter - clockwise), it would be \((- 1,3)\). Then after reflection across the \(x\) - axis \((-1,-3)\) which is \(J'(-1,-3)\) (matches the graph).

Step2: Determine the reflection rule

The rule for reflection across the \(x\) - axis is \((x,y)\to(x, - y)\).

Answer:

Rotation: \((x,y)\to(-y,x)\)
Reflection: \((x,y)\to(x, - y)\)