Question

test prep dilate abcd with a scale factor of 2 and center (0, 0). use the polygon tool to plot the image.

Explanation:

Step1: Recall dilation formula

If the center of dilation is the origin \((0,0)\) and the scale - factor is \(k\), the transformation rule for a point \((x,y)\) is \((x,y)\to(kx,ky)\). Here \(k = 2\).

Step2: Identify vertices of polygon ABCD

Let's assume the vertices of polygon \(ABCD\) are \(A(x_1,y_1)\), \(B(x_2,y_2)\), \(C(x_3,y_3)\), \(D(x_4,y_4)\). From the graph, if \(A=(0, - 2)\), \(B=(2,-1)\), \(C=(2,1)\), \(D=(0, - 2)\) (assuming the lower - left vertex is \(A\) and going counter - clockwise).

Step3: Apply dilation formula to each vertex

For \(A=(0,-2)\), \(A'=(2\times0,2\times(-2))=(0, - 4)\)
For \(B=(2,-1)\), \(B'=(2\times2,2\times(-1))=(4,-2)\)
For \(C=(2,1)\), \(C'=(2\times2,2\times1)=(4,2)\)
For \(D=(0,-2)\), \(D'=(2\times0,2\times(-2))=(0,-4)\)

Answer:

Plot the points \((0, - 4)\), \((4,-2)\), \((4,2)\), \((0,-4)\) and connect them to form the dilated polygon.