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. what does the scale factor tell you about the location of point b on the dilated image? the scale factor is?, so point b is? cm away from the origin.

Explanation:

Step1: Recall the property of dilation

When a point is dilated with the center of dilation at the origin and a scale factor \(k\), the distance from the origin of the dilated point \(P'\) is \(k\) times the distance from the origin of the original point \(P\).

Step2: Identify the scale factor

The scale factor \(k = 2\) (given in the problem statement: "Dilate the paper - clip by a scale factor of 2").

Step3: Calculate the distance of \(B'\) from the origin

We know that the distance of \(B\) from the origin \(d(B)=4\) cm. Using the formula \(d(B')=k\times d(B)\), substitute \(k = 2\) and \(d(B)=4\). So \(d(B')=2\times4\).

Answer:

The scale factor is \(2\), so point \(B'\) is \(8\) cm away from the origin.