Question

triangle abc is similar to triangle xyz. the triangles are shown below. 11 part a what is the scale factor for the dilation of triangle abc? explain how you determined your answer.

Explanation:

Step1: Identify corresponding side - lengths

Let's assume we can find the lengths of corresponding sides of \(\triangle ABC\) and \(\triangle XYZ\) using the grid. For example, if the length of a side of \(\triangle ABC\) is \(a\) and the length of the corresponding side of \(\triangle XYZ\) is \(b\).

Step2: Calculate the scale - factor

The scale factor \(k\) of the dilation from \(\triangle ABC\) to \(\triangle XYZ\) is given by the ratio of the lengths of corresponding sides, \(k=\frac{b}{a}\). Suppose the length of a side of \(\triangle ABC\) is \(2\) units and the length of the corresponding side of \(\triangle XYZ\) is \(4\) units. Then \(k = \frac{4}{2}=2\).

Answer:

The scale factor is found by taking the ratio of the lengths of corresponding sides of \(\triangle XYZ\) and \(\triangle ABC\). For example, if the length of a side of \(\triangle ABC\) is \(s_1\) and the length of the corresponding side of \(\triangle XYZ\) is \(s_2\), the scale factor \(k=\frac{s_2}{s_1}\). Without specific side - length values from the grid, we can't give a numerical answer, but the method is as described.