Question

in the figure, polygon abcd is dilated by a factor of 2 to produce abcd with the origin as the center of dilation. point a is at , and point d is at

Explanation:

Step1: Find the coordinates of point A and D

From the graph, point \(A(-1,-1)\) and point \(D(2,-1)\)

Step2: Apply the dilation formula

The formula for dilation with center at the origin and scale factor \(k\) is \((x,y)\to(kx,ky)\). Here \(k = 2\)
For point \(A(-1,-1)\), after dilation \(A'=(2\times(-1),2\times(-1))=(-2,-2)\)
For point \(D(2,-1)\), after dilation \(D'=(2\times2,2\times(-1))=(4,-2)\)

Answer:

Point \(A'\) is at \((-2,-2)\), and point \(D'\) is at \((4,-2)\)