Question

quadrilateral abcd is shown below. what are the coordinates of point d if quadrilateral abcd is dilated with scale factor ⅔ and center (0, 0)?

Explanation:

Step1: Identify the coordinates of point D

From the graph, point D has coordinates (9, 6).

Step2: Apply the dilation formula

For a dilation with scale - factor $k=\frac{2}{3}$ and center of dilation at the origin $(0,0)$, the formula for the coordinates of a dilated point $(x',y')$ from the original point $(x,y)$ is $x' = kx$ and $y'=ky$. Here, $x = 9$ and $y = 6$, $k=\frac{2}{3}$. So $x'=\frac{2}{3}\times9 = 6$ and $y'=\frac{2}{3}\times6 = 4$.

Answer:

(6, 4)