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: Recall dilation formula

For a point $(x,y)$ dilated by a factor $k$ centered at the origin, the new - point $(x',y')$ is given by $(x',y')=(k x,k y)$. Here $k = \frac{1}{2}$.

Step2: Find new coordinates of point B

The coordinates of point B are $(- 6,0)$. Using the dilation formula, $x'=\frac{1}{2}\times(-6)=-3$ and $y'=\frac{1}{2}\times0 = 0$. So the new - point B' is $(-3,0)$.

Step3: Find new coordinates of point C

The coordinates of point C are $(-4,-4)$. Then $x'=\frac{1}{2}\times(-4)=-2$ and $y'=\frac{1}{2}\times(-4)=-2$. So the new - point C' is $(-2,-2)$.

Step4: Find new coordinates of point D

The coordinates of point D are $(4,-4)$. So $x'=\frac{1}{2}\times4 = 2$ and $y'=\frac{1}{2}\times(-4)=-2$. The new - point D' is $(2,-2)$.

Step5: Find new coordinates of point E

The coordinates of point E are $(4,6)$. Then $x'=\frac{1}{2}\times4 = 2$ and $y'=\frac{1}{2}\times6 = 3$. The new - point E' is $(2,3)$.

Step6: Find new coordinates of point F

The coordinates of point F are $(-2,4)$. So $x'=\frac{1}{2}\times(-2)=-1$ and $y'=\frac{1}{2}\times4 = 2$. The new - point F' is $(-1,2)$.

Step7: Plot the new - figure

Plot the points B'$(-3,0)$, C'$(-2,-2)$, D'$(2,-2)$, E'$(2,3)$, F'$(-1,2)$ and connect them in the same order as the original figure.

Answer:

Plot the points $(-3,0),(-2,-2),(2,-2),(2,3),(-1,2)$ and connect them to form the dilated figure.