Question

graph the image of $\triangle qrs$ after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

From the graph:
$Q(-2, 1)$, $R(3, 1)$, $S(-2, 2)$

Step2: Apply dilation rule

For dilation centered at origin with scale factor $k=4$, multiply each coordinate by 4:
New $Q'$: $(-2 \times 4, 1 \times 4) = (-8, 4)$
New $R'$: $(3 \times 4, 1 \times 4) = (12, 4)$
New $S'$: $(-2 \times 4, 2 \times 4) = (-8, 8)$

Step3: Plot and connect points

Plot $Q'(-8,4)$, $R'(12,4)$, $S'(-8,8)$; connect to form $\Delta Q'R'S'$.

Answer:

The coordinates of the dilated triangle are $Q'(-8, 4)$, $R'(12, 4)$, $S'(-8, 8)$. When plotted on the grid, these points form the image of $\Delta QRS$ after the dilation.