Question

dilate △fgh by a scale factor of 4 with the center of dilation at the origin. graph the dilation.

Explanation:

Step1: Find the coordinates of original points

From the graph, we can see that \(F(-3,1)\), \(G(-1,0)\), \(H(-1,-2)\)

Step2: Apply the dilation formula

The formula for dilation with center at the origin \((x,y)\to(kx,ky)\), where \(k = 4\)

• For point \(F(-3,1)\):

\(x=-3,y = 1,k = 4\)
\(x'=4\times(-3)=-12,y'=4\times1 = 4\), so \(F'(-12,4)\)

• For point \(G(-1,0)\):

\(x=-1,y = 0,k = 4\)
\(x'=4\times(-1)=-4,y'=4\times0=0\), so \(G'(-4,0)\)

• For point \(H(-1,-2)\):

\(x=-1,y=-2,k = 4\)
\(x'=4\times(-1)=-4,y'=4\times(-2)=-8\), so \(H'(-4,-8)\)

Step3: Plot the new points

Plot \(F'(-12,4)\), \(G'(-4,0)\) and \(H'(-4,-8)\) on the coordinate plane and connect them to form the dilated triangle \(\triangle F'G'H'\)

Answer:

The coordinates of the dilated triangle are \(F'(-12,4)\), \(G'(-4,0)\) and \(H'(-4,-8)\)