Question

figure below is dilated by a factor of 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 rule

For dilation centered at origin with scale factor $k$, $(x,y)\to(kx,ky)$. Here $k = 2$.

Step2: Identify original points

Identify the coordinates of points $H$, $J$ and $I$ on the original figure.

Step3: Calculate new coordinates

Multiply the $x$ - and $y$ - coordinates of each point by 2 to get the coordinates of the dilated points.

Step4: Plot new figure

Plot the new points and connect them to form the dilated figure.

Answer:

To dilate a point $(x,y)$ by a factor of $k = 2$ centered at the origin $(0,0)$, we use the rule $(x,y)\to(kx,ky)$.
Let's assume the coordinates of point $H$ are $(x_1,y_1)$, point $J$ are $(x_2,y_2)$ and point $I$ are $(x_3,y_3)$. After dilation, the new - coordinates will be $H'(2x_1,2y_1)$, $J'(2x_2,2y_2)$ and $I'(2x_3,2y_3)$.
For example, if $H=( - 2,-4)$, then $H'=( - 4,-8)$; if $J=(0,2)$, then $J'=(0,4)$; if $I=(3,1)$, then $I'=(6,2)$. Plot the new points $H'$, $J'$ and $I'$ and connect them to get the dilated figure.