Question

the figure below is dilated by a factor of 4 centered at the origin. plot the resulting image. click twice to plot a segment. click a segment to delete it. answer attempt 2 out of 2

Explanation:

Step1: Recall dilation rule

For a dilation centered at the origin with scale - factor \(k\), if a point \((x,y)\) is dilated, the new point \((x',y')\) is given by \((x',y')=(kx,ky)\). Here \(k = 4\).

Step2: Find new coordinates of point A

Point A has coordinates \((-1,-1)\). Using the dilation rule \((x',y')=(4\times(-1),4\times(-1))=(-4,-4)\).

Step3: Find new coordinates of point B

Point B has coordinates \((0, - 2)\). Using the dilation rule \((x',y')=(4\times0,4\times(-2))=(0,-8)\).

Step4: Find new coordinates of point C

Point C has coordinates \((2,-1)\). Using the dilation rule \((x',y')=(4\times2,4\times(-1))=(8,-4)\).

Step5: Find new coordinates of point D

Point D has coordinates \((1,1)\). Using the dilation rule \((x',y')=(4\times1,4\times1)=(4,4)\).

Step6: Find new coordinates of point E

Point E has coordinates \((0,2)\). Using the dilation rule \((x',y')=(4\times0,4\times2)=(0,8)\).

Step7: Plot the new points

Plot the points \((-4,-4)\), \((0,-8)\), \((8,-4)\), \((4,4)\), and \((0,8)\) on the coordinate - plane and connect them to form the dilated figure.

Since this is a plotting task and not possible to actually plot in this text - based format, the new coordinates of the vertices of the dilated figure are the key output.

Answer:

A'(-4,-4), B'(0,-8), C'(8,-4), D'(4,4), E'(0,8)