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 coordinates of K and K'

From the graph, \( K \) is at \( (8, 0) \) and \( K' \) is at \( (6, 0) \).

Step2: Calculate scale factor

The scale factor \( k \) for dilation is the ratio of the length of a side of the image (\( I'J'K' \)) to the corresponding side of the original (\( IJK \)). For the x - coordinate of \( K \) and \( K' \), the scale factor \( k=\frac{\text{Length of } K' \text{ - related side}}{\text{Length of } K \text{ - related side}}=\frac{6}{8}=\frac{3}{4} \). We can verify with other points too. For example, \( I \) is at \( (8, 8) \) and \( I' \) is at \( (6, 6) \). The ratio of the y - coordinates (or x - coordinates) is \( \frac{6}{8}=\frac{3}{4} \) (or \( \frac{6}{8}=\frac{3}{4} \) for x - coordinates).

Answer:

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