Question

rectangle abcd has vertices a(2, 4), b(6, 5), c(6, - 2), and d(2, - 2). a dilation with a scale factor of 4 and centered at the origin is applied to the rectangle. which vertex in the dilated image has coordinates of (8, 16)? a b c d

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor $k$, the coordinates of a point $(x,y)$ in the original figure are transformed to $(kx,ky)$. Here, $k = 4$.

Step2: Calculate dilated coordinates of point A

The coordinates of point $A$ are $(2,4)$. After dilation with a scale - factor of $4$, the new coordinates are $(4\times2,4\times4)=(8,16)$.

Step3: Calculate dilated coordinates of point B

The coordinates of point $B$ are $(6,5)$. After dilation, the new coordinates are $(4\times6,4\times5)=(24,20)$.

Step4: Calculate dilated coordinates of point C

The coordinates of point $C$ are $(6, - 2)$. After dilation, the new coordinates are $(4\times6,4\times(-2))=(24,-8)$.

Step5: Calculate dilated coordinates of point D

The coordinates of point $D$ are $(2, - 2)$. After dilation, the new coordinates are $(4\times2,4\times(-2))=(8,-8)$.

Answer:

A. $A'$