Question

the parallelogram ( uvwx ) is a dilation of the parallelogram ( 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: Find the length of \(VW\)

The \(x\) - coordinate of \(V\) is \(0\) and the \(x\) - coordinate of \(W\) is \(6\). So \(VW=\vert6 - 0\vert=6\) (using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\) as \(y\) - coordinates are same).

Step2: Find the length of \(V'W'\)

The \(x\) - coordinate of \(V'\) is \(0\) and the \(x\) - coordinate of \(W'\) is \(9\). So \(V'W'=\vert9 - 0\vert = 9\) (using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\) as \(y\) - coordinates are same).

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of image segment}}{\text{length of pre - image segment}}\). So \(k=\frac{V'W'}{VW}=\frac{9}{6}=\frac{3}{2}\)

Answer:

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