Question

1. a rectangle has vertices at (1,2), (1,5), (4,5), and (4,2). if the rectangle is dilated by a scale factor of 0.5 with the center of dilation at (0,0), what are the coordinates of the new vertices?

○ a. (2,4), (2,10), (8,10), (8,4)
○ b. (1,1), (1,2.5), (4,2.5), (4,1)
○ c. (0.5,1), (0.5,2.5), (2,2.5), (2,1)
○ d. (0.5,0.5), (1,1), (2,2), (2.5,2.5)

Explanation:

Step1: Apply dilation formula

When a point \((x,y)\) is dilated by a scale factor \(k\) with center of dilation at \((0,0)\), the new point is \((kx,ky)\). Here \(k = 0.5\).
For the point \((1,2)\): \((0.5\times1,0.5\times2)=(0.5,1)\)
For the point \((1,5)\): \((0.5\times1,0.5\times5)=(0.5,2.5)\)
For the point \((4,5)\): \((0.5\times4,0.5\times5)=(2,2.5)\)
For the point \((4,2)\): \((0.5\times4,0.5\times2)=(2,1)\)

Answer:

C. \((0.5,1),(0.5,2.5),(2,2.5),(2,1)\)