Question

the square ghij is a dilation of the square ghij. 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: Find length of side of original square

Count the units between \(G(-2,-4)\) and \(H(-6,-4)\) (or other adjacent vertices of square \(GHIJ\)). The length \(GH=\vert-2 - (-6)\vert = 4\) units.

Step2: Find length of side of dilated square

Count the units between \(G'(-2,-6)\) and \(H'(-8,-6)\) (or other adjacent vertices of square \(G'H'I'J'\)). The length \(G'H'=\vert-2-(-8)\vert = 6\) units.

Step3: Calculate scale factor

The scale factor \(k=\frac{\text{length of side of dilated figure}}{\text{length of side of original figure}}\). So \(k = \frac{6}{4}=\frac{3}{2}\)

Answer:

\(\frac{3}{2}\)