Question

the rectangle ( hijk ) is a dilation of the rectangle ( hijk ). what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole

Explanation:

Step1: Find the length of a side of the original rectangle

The original rectangle \(HIJK\). Let's consider the side \(HK\). The \(x -\)coordinate of \(H\) is \(- 8\) and the \(x -\)coordinate of \(K\) is \(4\). Using the distance formula for a horizontal line \(d=\vert x_2 - x_1\vert\), \(HK=\vert4-(-8)\vert=\vert4 + 8\vert = 12\).

Step2: Find the length of the corresponding side of the dilated rectangle

The dilated rectangle \(H'I'J'K'\). Consider the side \(H'K'\). The \(x -\)coordinate of \(H'\) is \(-10\) and the \(x -\)coordinate of \(K'\) is \(5\). Using the distance formula for a horizontal line \(d=\vert x_2 - x_1\vert\), \(H'K'=\vert5-(-10)\vert=\vert5 + 10\vert=15\).

Step3: Calculate the scale factor

The scale factor \(s\) of a dilation is given by \(s=\frac{\text{length of side of dilated figure}}{\text{length of side of original figure}}\). So \(s=\frac{15}{12}\). Simplify the fraction \(\frac{15}{12}=\frac{5\times3}{4\times3}=\frac{5}{4}\)

Answer:

\(\frac{5}{4}\)