Question

cal uses a computer program to resize photos for the online school newspaper. rectangle defg represents the photo. she drags the top right corner of the rectangle along the dashed line to form image rectangle defg. the center of dilation is at the origin. the scale factor is 1/2. a. what are the coordinates of the vertices of image rectangle defg? show your work.

Explanation:

Step1: Identify the coordinates of the original rectangle

Assume the coordinates of rectangle \(DEFG\) are \(D(1,1)\), \(E(8,1)\), \(F(8,10)\), \(G(1,10)\) (based on the grid - like structure in the image).

Step2: Apply the dilation formula

The formula for dilation with center at the origin \((x,y)\to(kx,ky)\) where \(k = \frac{1}{2}\).
For point \(D(1,1)\):
\(D'(1\times\frac{1}{2},1\times\frac{1}{2})=(\frac{1}{2},\frac{1}{2})\)
For point \(E(8,1)\):
\(E'(8\times\frac{1}{2},1\times\frac{1}{2})=(4,\frac{1}{2})\)
For point \(F(8,10)\):
\(F'(8\times\frac{1}{2},10\times\frac{1}{2})=(4,5)\)
For point \(G(1,10)\):
\(G'(1\times\frac{1}{2},10\times\frac{1}{2})=(\frac{1}{2},5)\)

Answer:

\(D'(\frac{1}{2},\frac{1}{2})\), \(E'(4,\frac{1}{2})\), \(F'(4,5)\), \(G'(\frac{1}{2},5)\)