Question

rectangle abcd has vertices a(8, 5), b(8, 10), c(14, 10), and d(14, 5). a dilation with a scale factor of 1.2 and centered at the origin is applied to the rectangle. which vertex in the dilated image has coordinates of (9.6, 6)?
a
b
c
d

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor \(k\), if a point \((x,y)\) is dilated, the new point \((x',y')\) is given by \(x' = kx\) and \(y'=ky\). Here \(k = 1.2\).

Step2: Check point A

For point \(A(8,5)\), \(x'=1.2\times8 = 9.6\) and \(y'=1.2\times5 = 6\).

Step3: Check point B

For point \(B(8,10)\), \(x'=1.2\times8 = 9.6\) and \(y'=1.2\times10 = 12\).

Step4: Check point C

For point \(C(14,10)\), \(x'=1.2\times14 = 16.8\) and \(y'=1.2\times10 = 12\).

Step5: Check point D

For point \(D(14,5)\), \(x'=1.2\times14 = 16.8\) and \(y'=1.2\times5 = 6\).

Answer:

A. \(A'\)