Question

plot the image of point d under a dilation about the origin (0,0) with a scale factor of 3.

Explanation:

Step1: Recall dilation formula

For a dilation about the origin with scale - factor $k$, if a point has coordinates $(x,y)$, its image has coordinates $(kx,ky)$. Here, $k = 3$ and the coordinates of point $D$ are $(-2,0)$.

Step2: Calculate new coordinates

Multiply the $x$ - coordinate and $y$ - coordinate of point $D$ by the scale factor. $x'=3\times(-2)=-6$ and $y'=3\times0 = 0$.

Answer:

The image of point $D$ has coordinates $(-6,0)$. Plot the point $(-6,0)$ on the $x$ - axis, 6 units to the left of the origin.