Question

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

Explanation:

Step1: Identify original vertices

Original coordinates:
$M(-1, 0)$, $N(-2, -1)$, $K(-1, -2)$, $L(2, -1)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor $k$, the new coordinate $(x', y')$ is $(k \cdot x, k \cdot y)$ where $k=4$.

• For $M$: $x' = 4 \cdot (-1) = -4$, $y' = 4 \cdot 0 = 0$
• For $N$: $x' = 4 \cdot (-2) = -8$, $y' = 4 \cdot (-1) = -4$
• For $K$: $x' = 4 \cdot (-1) = -4$, $y' = 4 \cdot (-2) = -8$
• For $L$: $x' = 4 \cdot 2 = 8$, $y' = 4 \cdot (-1) = -4$

Answer:

$M'(-4, 0)$, $N'(-8, -4)$, $K'(-4, -8)$, $L'(8, -4)$