Question

graph the image of rectangle klmn after a dilation with a scale factor of 3 with respect to the origin.

Explanation:

Step1: Identify original vertices

Original vertices: $K=(-3,-3)$, $L=(3,-3)$, $M=(3,1)$, $N=(-3,1)$

Step2: Apply dilation rule

Dilation formula: $(x,y) \to (3x, 3y)$

1. $K' = (3\times-3, 3\times-3) = (-9,-9)$
2. $L' = (3\times3, 3\times-3) = (9,-9)$
3. $M' = (3\times3, 3\times1) = (9,3)$
4. $N' = (3\times-3, 3\times1) = (-9,3)$

Step3: Plot new rectangle

Connect $K'(-9,-9)$, $L'(9,-9)$, $M'(9,3)$, $N'(-9,3)$

Answer:

The dilated rectangle has vertices $K'(-9,-9)$, $L'(9,-9)$, $M'(9,3)$, $N'(-9,3)$