Question

what is the image of (2, -7) after a dilation by a scale factor of 4 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 image point is $(kx,ky)$.

Step2: Identify values

Here $x = 2$, $y=-7$ and $k = 4$.

Step3: Calculate new coordinates

The new $x$-coordinate is $k\times x=4\times2 = 8$, and the new $y$-coordinate is $k\times y=4\times(-7)=-28$.

Answer:

$(8,-28)$