Question

dilate the line segment by a scale factor of 2 with a center of dilation at the origin. draw the dilated segment on the provided graph. drawing tools select point line segment click on a tool to begin drawing. delete undo reset

Explanation:

Step1: Recall the dilation formula

For a dilation with center at the origin \((0,0)\) and scale factor \(k\), if a point \(P(x,y)\) is dilated, the image \(P'(x',y')\) is given by \(x' = kx\) and \(y'=ky\). Here \(k = 2\).

Step2: Identify the endpoints of the original line - segment

The endpoints of the original line - segment are \((0,0)\) and \((4, - 5)\).

Step3: Apply the dilation formula to each endpoint

For the point \((0,0)\):
Using \(x'=kx\) and \(y' = ky\) with \(k = 2\), \(x'=2\times0 = 0\) and \(y'=2\times0=0\).
For the point \((4,-5)\):
Using \(x'=kx\) and \(y' = ky\) with \(k = 2\), \(x'=2\times4 = 8\) and \(y'=2\times(-5)=-10\).

Answer:

Draw a line - segment connecting the points \((0,0)\) and \((8, - 10)\) on the coordinate plane.