Question

use the drawing tool(s) to form the correct answer on the provided graph. dilate the given line segment by a scale factor of 0.5 with a center of dilation at the origin. draw the dilated segment on the provided graph.

Explanation:

Step1: Recall dilation formula

If the center of dilation is at the origin $(0,0)$ and the scale - factor is $k$, for a point $(x,y)$ the dilated point $(x',y')$ is given by $(x',y')=(k x,k y)$.

Step2: Identify endpoints of given line segment

The endpoints of the given line segment seem to be $(0,4)$ and $(0,6)$ (assuming the grid is of unit - length).

Step3: Apply dilation formula

For the point $(0,4)$ with $k = 0.5$, we have $(x',y')=(0.5\times0,0.5\times4)=(0,2)$.
For the point $(0,6)$ with $k = 0.5$, we have $(x',y')=(0.5\times0,0.5\times6)=(0,3)$.

Step4: Draw the dilated line segment

Draw a line segment between the points $(0,2)$ and $(0,3)$ on the provided graph.

Answer:

Draw a line segment on the graph with endpoints $(0,2)$ and $(0,3)$.