Question

the square rstu is a dilation of the square rstu. 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 the length of a side of original square

Count the units between \(R(-1,-2)\) and \(U(-1,-4)\) (or other adjacent vertices of square \(RSTU\)). The length of a side of square \(RSTU\) is \(|-2 - (-4)|= 2\) units.

Step2: Find the length of a side of dilated square

Count the units between \(R'(-5,-6)\) and \(U'(-5,-10)\) (or other adjacent vertices of square \(R'S'T'U'\)). The length of a side of square \(R'S'T'U'\) is \(|-6-(-10)| = 4\) units.

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side of image}}{\text{length of side of pre - image}}\). So \(k=\frac{4}{2}=2\)

Answer:

\(2\)