Question

triangle jkl was dilated using the rule d_{m,\frac{1}{3}}. the image, triangle jkl, is the result of the dilation. what is ll? 5 units 7.5 units 10 units 12.5 units

Explanation:

Step1: Recall dilation formula

If a figure is dilated with a scale factor \(k\), and the length of a segment in the original figure is \(L\), the length of the corresponding segment in the image is \(L'=L\times k\). Also, if \(ML'\) is \(2.5\) units and the scale factor \(k = \frac{1}{5}\) (since \(D_{M,\frac{1}{5}}\) is the dilation rule), and let \(ML=x\). Then \(ML'=x\times\frac{1}{5}\), so \(x = 2.5\times5=12.5\) units.

Step2: Calculate \(L'L\)

We know that \(ML = ML'+L'L\). Since \(ML = 12.5\) units and \(ML'=2.5\) units. Then \(L'L=ML - ML'\).

$$L'L=12.5 - 2.5$$

$$L'L = 10$$

Answer:

10 units