Question

a decagon is graphed on a coordinate grid and then dilated by a scale factor of 2/3 with the origin as the center of dilation. vertex a of the original decagon is located at (9, 6). write the ordered - pair that represents the location of vertex a after the dilation.

Explanation:

Step1: Recall dilation formula

For a dilation with center at the origin $(0,0)$ and scale - factor $k$, if a point $(x,y)$ is dilated, the new point $(x',y')$ is given by $(x',y')=(kx,ky)$. Here, $x = 9$, $y = 6$, and $k=\frac{2}{3}$.

Step2: Calculate the new $x$ - coordinate

$x'=k\times x=\frac{2}{3}\times9 = 6$.

Step3: Calculate the new $y$ - coordinate

$y'=k\times y=\frac{2}{3}\times6 = 4$.

Answer:

$(6,4)$