Question

the trapezoid mnop is a dilation of the trapezoid mnop. what is the scale factor of the dilation?

Explanation:

Step1: Find the length of a corresponding side

Let's take the vertical side \(OP\) and \(O'P'\).
The length of \(OP\) is \(10 - (- 0)=10\) (using the \(y\) - coordinates of \(O(5,10)\) and \(P(5,0)\)).
The length of \(O'P'\) is \(8-(- 0) = 8\) (using the \(y\) - coordinates of \(O'(4,8)\) and \(P'(4,0)\)).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of the image segment}}{\text{length of the pre - image segment}}\).
So, \(k=\frac{O'P'}{OP}\).
Substitute \(O'P' = 8\) and \(OP = 10\) into the formula: \(k=\frac{8}{10}=\frac{4}{5}\)

Answer:

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