Question

a quadrilateral with vertices at a(4, -4), b(4, -16), c(12, -16), and d(12, -4) has been dilated with a center at the origin. the image of d, point d, has coordinates (36, -12). what is the scale factor of the dilation?
options: $\frac{1}{9}$, $\frac{1}{3}$, 3, 9

Explanation:

Step1: Identify original and image points

Original point $D(12, -4)$, image $D'(36, -12)$

Step2: Calculate scale factor (x-coordinate)

$\text{Scale factor} = \frac{36}{12} = 3$

Step3: Verify with y-coordinate

$\text{Scale factor} = \frac{-12}{-4} = 3$
Wait correction: Wait no, 36/12=3, -12/-4=3. Wait no, wait 312=36, 3(-4)=-12. Oh wait, the option 3 is there? Wait no, wait 36 divided by 12 is 3, yes. Wait I misread earlier.

Wait correction:

Step1: Select corresponding coordinates

Original $D(12, -4)$, Image $D'(36, -12)$

Step2: Compute x-scale factor

$\text{Scale factor } k = \frac{36}{12} = 3$

Step3: Verify with y-coordinate

$k = \frac{-12}{-4} = 3$

Answer:

9