Question

a paper clip is shown on the graph. the distance from a to b represents the length of the paper clip. dilate the paper clip by a scale factor of 2 with the center of dilation at the origin. point b is 4 cm from the origin. the scale factor is 2, so point b is 8 cm away from the origin. what are the coordinates of point b? point b is at (?,?)

Explanation:

Step1: Determine the coordinates of point B

From the graph, point B is at \((4,0)\).

Step2: Apply the dilation formula

The formula for dilation with center at the origin \((x,y)\to(kx,ky)\), where \(k = 2\) (scale factor).
For point \(B(4,0)\), after dilation: \(x'=2\times4 = 8\), \(y'=2\times0=0\)

Answer:

\((8,0)\)