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.

Explanation:

Step1: Recall dilation formula

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 $(x',y')=(k x,k y)$. Here $k = 4$.

Step2: Find coordinates of dilated points

• Point $N(-1,0)$: After dilation, $N'=4\times(-1),4\times0=(-4,0)$.
• Point $P(2,0)$: After dilation, $P'=4\times2,4\times0=(8,0)$.
• Point $Q(0,2)$: After dilation, $Q'=4\times0,4\times2=(0,8)$.
• Point $O(1, - 2)$: After dilation, $O'=4\times1,4\times(-2)=(4,-8)$.
• Point $R(-2,1)$: After dilation, $R'=4\times(-2),4\times1=(-8,4)$.

Step3: Plot the points

Plot the points $N'(-4,0)$, $P'(8,0)$, $Q'(0,8)$, $O'(4,-8)$, $R'(-8,4)$ on the coordinate - plane and connect them in the same order as the original figure to get the dilated image.

Answer:

Plot the points $(-4,0)$, $(8,0)$, $(0,8)$, $(4,-8)$, $(-8,4)$ and connect them to form the dilated figure.