Question

1. polygon a has vertices at (4, -2), (-4, -2) and (0, 6). the polygon will be dilated with respect to the origin by a scale factor of 2. what will be the coordinates of the image of polygon a? a. (8, -4), (-8, -4), (0, 12) b. (2, -1), (-2, -1), (0, 3) c. (16, -8), (-16, -8), (0, 24) d. (1, -2), (-1, -2), (0, 3)

Explanation:

Step1: Apply dilation formula

When a point \((x,y)\) is dilated with respect to the origin by a scale factor \(k\), the new coordinates are \((kx,ky)\). Here \(k = 2\).
For the point \((4,-2)\):
\((2\times4,2\times(-2))=(8,-4)\)

Step2: Apply dilation formula for second point

For the point \((-4,-2)\):
\((2\times(-4),2\times(-2))=(-8,-4)\)

Step3: Apply dilation formula for third point

For the point \((0,6)\):
\((2\times0,2\times6)=(0,12)\)

Answer:

A. \((8, - 4),(-8,-4),(0,12)\)