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? use the number pad to enter your answers in the boxes. d( , )

Explanation:

Step1: Find coordinates after dilation

The formula for dilation with scale - factor $k$ centered at the origin is $(x,y)\to(kx,ky)$. Given $k = \frac{1}{2}$ and the coordinates of $D$ are $(- 6,2)$. After dilation, $D'$ has coordinates $(\frac{1}{2}\times(-6),\frac{1}{2}\times2)=(-3,1)$.

Step2: Find coordinates after translation

The formula for a translation of $3$ units down is $(x,y)\to(x,y - 3)$. For point $D'(-3,1)$, after translation, the $x$ - coordinate remains the same and the $y$ - coordinate is $1-3=-2$. So the coordinates of $D''$ are $(-3,-2)$.

Answer:

$D''(-3,-2)$