Question

the 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

If a point $(x,y)$ is dilated by a factor $k$ centered at the origin, the new - point is $(kx,ky)$. Here $k = 2$.

Step2: Identify original points

Let's assume the vertices of the triangle are $D(x_1,y_1)$, $E(x_2,y_2)$, $F(x_3,y_3)$. Suppose $D(-1,-3)$, $E(2,0)$, $F(-1,1)$.

Step3: Calculate new points

For point $D$: New coordinates are $(2\times(-1),2\times(-3))=(-2,-6)$.
For point $E$: New coordinates are $(2\times2,2\times0)=(4,0)$.
For point $F$: New coordinates are $(2\times(-1),2\times1)=(-2,2)$.

Step4: Plot new points

Plot the points $(-2,-6)$, $(4,0)$ and $(-2,2)$ and connect them to form the dilated triangle.

Since this is a plotting task and we can't actually perform the plot in this text - based format, the steps above show how to find the coordinates of the dilated figure. If you were to plot on a graph paper or using a graphing tool, you would use the calculated coordinates $(-2,-6)$, $(4,0)$ and $(-2,2)$ to draw the dilated triangle.

Answer:

Step1: Recall dilation rule

If a point $(x,y)$ is dilated by a factor $k$ centered at the origin, the new - point is $(kx,ky)$. Here $k = 2$.

Step2: Identify original points

Let's assume the vertices of the triangle are $D(x_1,y_1)$, $E(x_2,y_2)$, $F(x_3,y_3)$. Suppose $D(-1,-3)$, $E(2,0)$, $F(-1,1)$.

Step3: Calculate new points

For point $D$: New coordinates are $(2\times(-1),2\times(-3))=(-2,-6)$.
For point $E$: New coordinates are $(2\times2,2\times0)=(4,0)$.
For point $F$: New coordinates are $(2\times(-1),2\times1)=(-2,2)$.

Step4: Plot new points

Plot the points $(-2,-6)$, $(4,0)$ and $(-2,2)$ and connect them to form the dilated triangle.

Since this is a plotting task and we can't actually perform the plot in this text - based format, the steps above show how to find the coordinates of the dilated figure. If you were to plot on a graph paper or using a graphing tool, you would use the calculated coordinates $(-2,-6)$, $(4,0)$ and $(-2,2)$ to draw the dilated triangle.