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. complete the statement. point a is cm up from point b, so point a is 7 cm up from point b.

Explanation:

Step1: Analyze the original distance

Count the vertical units from point \(B\) to point \(A\) on the graph. There are \(3.5\) cm from \(B\) to \(A\).

Step2: Apply the dilation rule

When dilating by a scale factor \(k = 2\) with the center of dilation at the origin, the distance between corresponding points (in this case \(A'\) and \(B'\)) is \(k\) times the original distance. So we calculate \(3.5\times2\).

$$3.5\times2=\frac{35}{10}\times2=\frac{70}{10} = 7$$

Answer:

Point \(A\) is \(3.5\) cm up from point \(B\), so point \(A'\) is \(7\) cm up from point \(B'\). The first blank is \(3.5\).