Question

1. angel placed a rectangular photograph on a page of the yearbook. rectangle abcd, shown on the coordinate grid below, represents the location of the photograph on the yearbook page. angel dilates the photograph, rectangle abcd, by a scale factor of 1/2 with the center of dilation at the origin to form rectangle abcd and then translates rectangle abcd 3 units down to form rectangle abcd. what are the coordinates of vertex d?

Explanation:

Step1: Find coordinates of \(D\)

From the grid, the coordinates of \(D\) are \((-4,2)\)

Step2: Apply dilation

Dilation with scale factor \(\frac{1}{2}\) and center at origin \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\).
For \(D(-4,2)\), after dilation \(D'(\frac{1}{2}\times(-4),\frac{1}{2}\times2)=(-2,1)\)

Step3: Apply translation

Translation \(3\) units down: \((x,y)\to(x,y - 3)\)
For \(D'(-2,1)\), after translation \(D''(-2,1-3)=(-2,-2)\)

Answer:

\((-2,-2)\)