Question

interactive practice: perform and describe transformations involving dilations
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.
list the coordinates of the vertices of figure $abcd$.
after dilation after translation
$a(2, - 2)$ ?
$b(2, - 8)$ $a(-4, - 2)$
$c(6, - 8)$ $a(4, - 2)$
$d(6, - 2)$ $a(2, - 4)$
$a(2,0)$

Explanation:

Step1: Recall translation rule

For a translation 2 units to the right, we add 2 to the x - coordinate of each point.

Step2: Calculate new coordinates for \(A'\)

Given \(A'(2,-2)\), new \(x = 2 + 2=4\), \(y=-2\). So \(A''(4,-2)\).

Step3: Calculate new coordinates for \(B'\)

Given \(B'(2,-8)\), new \(x = 2+ 2 = 4\), \(y=-8\). So \(B''(4,-8)\).

Step4: Calculate new coordinates for \(C'\)

Given \(C'(6,-8)\), new \(x = 6+ 2 = 8\), \(y=-8\). So \(C''(8,-8)\).

Step5: Calculate new coordinates for \(D'\)

Given \(D'(6,-2)\), new \(x = 6+ 2 = 8\), \(y=-2\). So \(D''(8,-2)\).

Answer:

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