Question

list the coordinates of the vertices of figure abcd.
figure abcd is dilated by a scale factor of 2 with a center of dilation at the origin. then, the image is translated 2 units to the right.

Explanation:

Step1: Apply dilation formula

For a dilation with scale factor \(k = 2\) centered at the origin \((x,y)\to(kx,ky)\).
For point \(A(1, - 1)\): \((1\times2,-1\times2)=(2,-2)\)
For point \(B(1,-4)\): \((1\times2,-4\times2)=(2,-8)\)
For point \(C(3,-4)\): \((3\times2,-4\times2)=(6,-8)\)
For point \(D(3,-1)\): \((3\times2,-1\times2)=(6,-2)\)

Step2: Apply translation formula

For a translation \(2\) units to the right \((x,y)\to(x + 2,y)\)
For \(A'(2,-2)\): \((2+2,-2)=(4,-2)\)
For \(B'(2,-8)\): \((2 + 2,-8)=(4,-8)\)
For \(C'(6,-8)\): \((6+2,-8)=(8,-8)\)
For \(D'(6,-2)\): \((6+2,-2)=(8,-2)\)

Answer:

\(A'(4,-2)\), \(B'(4,-8)\), \(C'(8,-8)\), \(D'(8,-2)\)