Question

what is the image of (4, 8) after a dilation by a scale factor of 5 centered at the origin?

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale factor $k$, if the original point is $(x,y)$, the new point $(x',y')$ is given by $(x',y')=(k\times x,k\times y)$.

Step2: Substitute values

Here, $x = 4$, $y = 8$ and $k = 5$. So $x'=5\times4 = 20$ and $y'=5\times8=40$.

Answer:

$(20,40)$