Question

v, geometry sem a geometry
ons
line segment qr is dilated to create line segment qr using the dilation
rule d_{1,1.5}
what is y, the distance between points r and r?
4 units
3 units
6 units
9 units

Explanation:

Step1: Recall the dilation formula

If a figure is dilated with a scale factor \(k\), and the original length is \(l\), the new length is \(l'=kl\). Here, the scale factor \(k = 1.5\) (since \(QT\) is dilated to \(Q'T'\) and the general dilation rule \(D_{1.5}\) is given). The length of \(RT\) is \(8\) units. After dilation, the length of \(R'T'\) is \(1.5\times8=12\) units.

Step2: Calculate the distance \(y\)

We know that \(y=R'T'-RT\). Substitute \(R'T' = 12\) and \(RT = 8\) into the formula. So \(y=12 - 8=4\) units.

Answer:

4 units