Question

6 sarah draws figure efgh in the coordinate plane. she rotates figure efgh 90° clockwise around vertex e to form image efgh. draw the image efgh on the coordinate plane.
7 △pqr has vertices p(-4,4), q(-2,3), and r(-5,2). △pqr is rotated 90° clockwise around the origin. then the image is translated 5 units down and reflected across the y-axis. what are the coordinates of the vertices of △pqr? show your work

Explanation:

Step1: Apply rotation formula

The rule for a \(90^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, -x)\).
For \(P(-4,4)\): \(P'(4,4)\)
For \(Q(-2,3)\): \(Q'(3,2)\)
For \(R(-5,2)\): \(R'(2,5)\)

Step2: Apply translation

The rule for translation \(5\) units down \((x,y)\to(x,y - 5)\).
For \(P'(4,4)\): \(P''(4,-1)\)
For \(Q'(3,2)\): \(Q''(3,-3)\)
For \(R'(2,5)\): \(R''(2,0)\)

Step3: Apply reflection

The rule for reflection across the \(y\) - axis \((x,y)\to(-x,y)\).
For \(P''(4,-1)\): \(P'''(-4,-1)\)
For \(Q''(3,-3)\): \(Q'''(-3,-3)\)
For \(R''(2,0)\): \(R'''(-2,0)\)

Answer:

The coordinates of the vertices are \(P'''(-4,-1)\), \(Q'''(-3,-3)\), \(R'''(-2,0)\)