Question

dilate ( efgh ) by a scale factor of 2 with a center of dilation at the origin.

Explanation:

Step1: Recall the dilation formula

If a point \((x,y)\) is dilated by a scale factor \(k\) with center of dilation at the origin \((0,0)\), the new point \((x',y')\) is given by \((x',y')=(kx,ky)\).

Step2: Find the coordinates of \(E'\), \(F'\), \(G'\), \(H'\)

From the graph:

• Coordinates of \(E'=(0,1)\), after dilation: \((0\times2,1\times 2)=(0,2)\)
• Coordinates of \(F'=(-4,1)\), after dilation: \((-4\times2,1\times2)=(-8,2)\)
• Coordinates of \(G'=(-4,3)\), after dilation: \((-4\times2,3\times2)=(-8,6)\)
• Coordinates of \(H'=(0,3)\), after dilation: \((0\times2,3\times2)=(0,6)\)

Answer:

The coordinates of the dilated figure \(E''F''G''H''\) are \(E''(0,2)\), \(F''(-8,2)\), \(G''(-8,6)\), \(H''(0,6)\)