Question

1. label the x and y axes.
2. label each of the points in the pre - image. list the points in the pre - image
3. rotate the figure 270° counterclockwise. write the rule associated with the transformation.
4. what are the points of the image?
5. label the x and y axes.
6. label each of the points in the pre - image. list the points in the pre - image
7. rotate the figure 270° clockwise. write the rule associated with the transformation.
8. what are the points of the image?

Explanation:

Step 1: Label axes and points in pre - image

From the grid, assume the points of the pre - image are \(A(3,1)\), \(B(5,1)\), \(C(3, - 1)\), \(D(5,-1)\)

Step 2: Determine rotation rule

The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(y, - x)\)

Step 3: Apply rotation rule to find image points

For point \(A(3,1)\): \((3,1)\to(1,-3)\)
For point \(B(5,1)\): \((5,1)\to(1,-5)\)
For point \(C(3, - 1)\): \((3,-1)\to(-1,-3)\)
For point \(D(5,-1)\): \((5,-1)\to(-1,-5)\)

Answer:

The points of the image are \((1,-3)\), \((1,-5)\), \((-1,-3)\), \((-1,-5)\)