Question

1. $k(-2.5, -0.5)$ is the image of $p$ after a dilation centered at the origin with a scale factor of $1/4$. what are the coordinates of $k$?

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated by a scale - factor $k$ centered at the origin, the image is $(kx,ky)$. Here we know the image $(x',y')$ and $k$, and we want to find the original point $(x,y)$. So, $x=\frac{x'}{k}$ and $y = \frac{y'}{k}$.

Step2: Calculate the x - coordinate of the original point

Given $x'=-2.5$ and $k = \frac{1}{4}$, then $x=\frac{-2.5}{\frac{1}{4}}=-2.5\times4=-10$.

Step3: Calculate the y - coordinate of the original point

Given $y'=-0.5$ and $k=\frac{1}{4}$, then $y=\frac{-0.5}{\frac{1}{4}}=-0.5\times4 = - 2$.

Answer:

$(-10,-2)$