Question

question
the figure below is dilated by a factor of \\( \frac { 1 } { 2 } \\) centered at the origin. plot the resulting image.
click twice to plot a segment.
click a segment to delete it.

Explanation:

Step1: Find the coordinates of original points

Assume the coordinates of points \(B(-6,0)\), \(C(-4,-4)\), \(D(6,-4)\), \(E(4,6)\), \(F(-4,4)\)

Step2: Apply the dilation formula

The dilation formula centered at the origin is \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)
For point \(B(-6,0)\): \((\frac{1}{2}\times(-6),\frac{1}{2}\times0)=(-3,0)\)
For point \(C(-4,-4)\): \((\frac{1}{2}\times(-4),\frac{1}{2}\times(-4))=(-2,-2)\)
For point \(D(6,-4)\): \((\frac{1}{2}\times6,\frac{1}{2}\times(-4))=(3,-2)\)
For point \(E(4,6)\): \((\frac{1}{2}\times4,\frac{1}{2}\times6)=(2,3)\)
For point \(F(-4,4)\): \((\frac{1}{2}\times(-4),\frac{1}{2}\times4)=(-2,2)\)

Step3: Plot the new points

Plot the points \((-3,0)\), \((-2,-2)\), \((3,-2)\), \((2,3)\), \((-2,2)\) and connect them in the same order as the original figure.

Answer:

Plot the points \((-3,0)\), \((-2,-2)\), \((3,-2)\), \((2,3)\), \((-2,2)\) and connect them.