Question

1. p(12, -3) is the image of p after a dilation centered at the origin with a scale factor of 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 $y'=ky$. Here $k = 3$, $x'=12$, and $y'=-3$.

Step2: Solve for $x$

We know that $x' = kx$. Substituting $x' = 12$ and $k = 3$ into the formula, we get $12=3x$. Solving for $x$ gives $x=\frac{12}{3}=4$.

Step3: Solve for $y$

We know that $y' = ky$. Substituting $y'=-3$ and $k = 3$ into the formula, we get $-3 = 3y$. Solving for $y$ gives $y=\frac{-3}{3}=-1$.

Answer:

$(4,-1)$