Question

p(12, -3) is the image of p after a dilation centered at the origin with a scale factor of k = 3. what are the coordinates of p.

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor $k$, if a point $P(x,y)$ is dilated to $P'(x',y')$, then $x' = kx$ and $y' = ky$. We need to find the original point $P(x,y)$ given $P'(x',y')$ and $k$.

Step2: Solve for $x$

Given $x' = 12$ and $k = 3$, from $x'=kx$, we can solve for $x$ by dividing both sides of the equation by $k$. So $x=\frac{x'}{k}=\frac{12}{3}=4$.

Step3: Solve for $y$

Given $y'=- 3$ and $k = 3$, from $y' = ky$, we can solve for $y$ by dividing both sides of the equation by $k$. So $y=\frac{y'}{k}=\frac{-3}{3}=-1$.

Answer:

$(4,-1)$