Question

the trapezoid ( rstu ) is a dilation of the trapezoid ( 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

Explanation:

Step1: Find the length of a corresponding side

Take the vertical side of the trapezoid. For trapezoid \(RSTU\), the length of the vertical side (e.g., from \(R(-6,6)\) to \(U(-6, - 6)\)) is \(|6-(-6)|=12\). For trapezoid \(R'S'T'U'\), the length of the corresponding vertical side (e.g., from \(R'(-2,2)\) to \(U'(-2,-2)\)) is \(|2 - (-2)| = 4\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). So \(k=\frac{4}{12}\). Simplifying \(\frac{4}{12}\) by dividing both the numerator and denominator by their greatest common divisor (which is 4), we get \(k = \frac{1}{3}\).

Answer:

\(\frac{1}{3}\)