Question

given the coordinates of the pre - image, find the coordinates of the image.
$h(-10,-1),i(-10,-7),j(-4,-1)$

• refletion about the y - axis, followed by rotation $90^{circ}$ about the origin

$h(square,square)$
$i(square,square)$
$j(square,square)$

Explanation:

Step1: Reflection about the y - axis

The rule for reflection about the y - axis is \((x,y)\to(-x,y)\).
For point \(H(-10,-1)\), after reflection \(H'(10,-1)\).
For point \(I(-10,-7)\), after reflection \(I'(10,-7)\).
For point \(J(-4,-1)\), after reflection \(J'(4,-1)\).

Step2: Rotation \(90^{\circ}\) about the origin

The rule for rotation \(90^{\circ}\) about the origin is \((x,y)\to(-y,x)\).
For point \(H'(10,-1)\), after rotation \(H''(1,10)\).
For point \(I'(10,-7)\), after rotation \(I''(7,10)\).
For point \(J'(4,-1)\), after rotation \(J''(1,4)\).

Answer:

\(H''(1,10)\), \(I''(7,10)\), \(J''(1,4)\)