Question

the trapezoid opqr is a dilation of the trapezoid opqr. 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 coordinates of corresponding points

Let's take a pair of corresponding points. For example, if we consider point \(Q\) and \(Q'\). Suppose \(Q\) has coordinates \((x_1,y_1)\) and \(Q'\) has coordinates \((x_2,y_2)\). From the graph, assume \(Q=(10,5)\) and \(Q'=(8,4)\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of a side in the image}}{\text{length of the corresponding side in the pre - image}}\) or \(k = \frac{\text{coordinate of a point in the image}}{\text{coordinate of the corresponding point in the pre - image}}\) (assuming the center of dilation is the origin). Using the \(y\) - coordinates (or \(x\) - coordinates) of \(Q\) and \(Q'\), \(k=\frac{4}{5}\)

Answer:

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