Question

1. what is the image of the point (4, -1) after a dilation with a scale factor of 3 centered at the origin?

a. (12, -3)
b. (3, -12)
c. (4, -1)
d. (1.33, -0.33)

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor $k$, if the original point is $(x,y)$, the image point is $(kx,ky)$.

Step2: Identify values

Here, $x = 4$, $y=-1$, and $k = 3$.

Step3: Calculate new coordinates

$kx=3\times4 = 12$ and $ky=3\times(-1)=-3$. So the image point is $(12, -3)$.

Answer:

A. $(12, -3)$