Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of point $K$ are $(0, - 2)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, the formula to find the new coordinates $(x',y')$ of a point $(x,y)$ is $(x',y')=(k\cdot x,k\cdot y)$. Here $k = 4$, $x = 0$, and $y=-2$.
$x'=4\times0 = 0$
$y'=4\times(-2)=-8$

Answer:

$K'(0,-8)$