Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify original vertices

From the graph:
$R = (-4, -3)$, $Q = (-6, -3)$, $S = (-6, 1)$

Step2: Apply dilation rule

For a dilation centered at the origin with scale factor $k$, a point $(x,y)$ becomes $(k \cdot x, k \cdot y)$. Here $k=2$.

• For $R$: $(2 \cdot -4, 2 \cdot -3) = (-8, -6)$
• For $Q$: $(2 \cdot -6, 2 \cdot -3) = (-12, -6)$
• For $S$: $(2 \cdot -6, 2 \cdot 1) = (-12, 2)$

Answer:

$R' = (-8, -6)$, $Q' = (-12, -6)$, $S' = (-12, 2)$