Question

answer all parts of the question on the graph to the right. plot the pre - image and label it appropriately. make sure to show the transformations using different colors and labeling them appropriately. show the line of reflection when reflecting.

• plot the pre - image, triangle wxy: w(0, 4), x(-2, -2), y(1, -3).
• then, rotate the triangle 270° clockwise about the origin creating the image wxy.
• then, reflect wxy across y = -x creating image wxy

Explanation:

Step1: Recall rotation rule

The rule for a \(270^{\circ}\) clock - wise rotation about the origin \((x,y)\to(y, - x)\).
For point \(W(0,4)\): \(W'(4,0)\)
For point \(X(-2,-2)\): \(X'(-2,2)\)
For point \(Y(1,-3)\): \(Y'(-3,-1)\)

Step2: Recall reflection rule

The rule for reflecting a point \((x,y)\) across the line \(y=-x\) is \((x,y)\to(-y,-x)\).
For point \(W'(4,0)\): \(W''(0, - 4)\)
For point \(X'(-2,2)\): \(X''(-2,2)\)
For point \(Y'(-3,-1)\): \(Y''(1,3)\)

Answer:

Pre - image: \(W(0,4)\), \(X(-2,-2)\), \(Y(1,-3)\)
Image after rotation: \(W'(4,0)\), \(X'(-2,2)\), \(Y'(-3,-1)\)
Image after reflection: \(W''(0, - 4)\), \(X''(-2,2)\), \(Y''(1,3)\)
(Note: To complete the full task as required in the problem, you would need to actually plot these points on a graph, use different colors for the pre - image, rotated image and reflected image, and label them appropriately as well as show the line \(y =-x\) for the reflection step. But the above provides the coordinate - based solution for the geometric transformations.)