Question

the triangle ijk is a dilation of the triangle ijk. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Identify corresponding side lengths

Let's consider the vertical sides from \(K'\) to \(I'\) and from \(K\) to \(I\). The length of the vertical side from \(K'\) to \(I'\) is \(6\) (since \(y - \text{coordinate of }I'=6\) and \(y - \text{coordinate of }K' = 0\)), and the length of the vertical side from \(K\) to \(I\) is \(8\) (since \(y - \text{coordinate of }I = 8\) and \(y - \text{coordinate of }K=0\)).

Step2: Calculate the scale - factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side in the dilated figure to the length of the corresponding side in the original figure. So \(k=\frac{\text{length of side in }I'J'K'}{\text{length of side in }IJK}\). Using the vertical sides we identified, \(k = \frac{6}{8}=\frac{3}{4}\).

Answer:

\(\frac{3}{4}\)