Question

the square uvwx is a dilation of the square uvwx. 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: Determine the side length of the original square

Count the units between two adjacent vertices of square \(UVWX\). For example, between \(U\) and \(V\), the side - length \(s_{1}\) of square \(UVWX\):
If \(U\) is at \((- 5,-1)\) and \(V\) is at \((-3,-1)\), then \(s_{1}=\vert-3-(-5)\vert = 2\) units.

Step2: Determine the side length of the dilated square

Count the units between two adjacent vertices of square \(U'V'W'X'\). For example, between \(U'\) and \(V'\), if \(U'\) is at \((-4, - 2)\) and \(V'\) is at \((-3,-2)\), then the side - length \(s_{2}\) of square \(U'V'W'X'\) is \(s_{2}=\vert-3-(-4)\vert=1\) unit.

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of the image segment}}{\text{length of the pre - image segment}}\).
So, \(k = \frac{s_{2}}{s_{1}}\)
Substitute \(s_{1} = 2\) and \(s_{2}=1\) into the formula: \(k=\frac{1}{2}\)

Answer:

\(\frac{1}{2}\)