Question

the parallelogram ( stuv ) is a dilation of the parallelogram ( stuv ). 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 parallelogram

For parallelogram \(STUV\), let's consider the side \(ST\). The coordinates of \(S=(0,1)\) and \(T=(2,1)\). Using the distance formula for horizontal lines (since \(y -\)coordinates are the same), \(d=\vert x_2 - x_1\vert\). So, \(ST=\vert2 - 0\vert=2\).

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

For parallelogram \(S'T'U'V'\), consider the side \(S'T'\). The coordinates of \(S'=(0,5)\) and \(T'=(8,5)\). Using the distance formula for horizontal lines (since \(y -\)coordinates are the same), \(d=\vert x_2 - x_1\vert\). So, \(S'T'=\vert8 - 0\vert = 8\).

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). Substituting the values, \(k=\frac{S'T'}{ST}\). Since \(S'T' = 8\) and \(ST=2\), then \(k=\frac{8}{2}=4\).

Answer:

\(4\)