a rectangle has vertices (6,4), (2,4), (6, -2), and (2, -2). what are the coordinates of the vertices of the…

a rectangle has vertices (6,4), (2,4), (6, -2), and (2, -2). what are the coordinates of the vertices of the image after a dilation with the origin at its center and a scale factor of 1.5?\n\na. (3,2), (1,2), (3,-1), and (1,-1)\n\nb. (12,8), (4,8), (12,-4), and (4,-4)\n\nc. (9,6), (3,6), (9,-3), and (3,-3)\n\nd. (15,10), (5,10), (15,-5), and (5,-5)

a rectangle has vertices (6,4), (2,4), (6, -2), and (2, -2). what are the coordinates of the vertices of the image after a dilation with the origin at its center and a scale factor of 1.5?\n\na. (3,2), (1,2), (3,-1), and (1,-1)\n\nb. (12,8), (4,8), (12,-4), and (4,-4)\n\nc. (9,6), (3,6), (9,-3), and (3,-3)\n\nd. (15,10), (5,10), (15,-5), and (5,-5)

Answer

Answer:

c. (9,6), (3,6), (9,−3), and (3,−3)

Explanation:

Step1: Recall dilation rule

For dilation with origin as center and scale factor $k$, each vertex $(x,y)$ becomes $(k \cdot x, k \cdot y)$. Here $k=1.5$.

Step2: Dilate (6,4)

$\text{New coordinate} = (1.5 \times 6, 1.5 \times 4) = (9, 6)$

Step3: Dilate (2,4)

$\text{New coordinate} = (1.5 \times 2, 1.5 \times 4) = (3, 6)$

Step4: Dilate (6,-2)

$\text{New coordinate} = (1.5 \times 6, 1.5 \times (-2)) = (9, -3)$

Step5: Dilate (2,-2)

$\text{New coordinate} = (1.5 \times 2, 1.5 \times (-2)) = (3, -3)$