The trapezoid M'N'O'P' is a dilation of the trapezoid MNOP. What is the scale factor of the dilation? Simplify your answer and write it as a proper fraction, an improper fraction,... The trapezoid M'N'O'P' is a dilation of the trapezoid MNOP. 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. Read more

Steps to Solve

1. Identify Corresponding Vertices
   The corresponding vertices of trapezoids $MNOP$ and $M'N'O'P'$ are as follows:

   • $M(-8, -4) \rightarrow M'(-8, -8)$
   • $N(-4, -2) \rightarrow N'(-8, -2)$
   • $O(2, 2) \rightarrow O'(2, 6)$
   • $P(4, -2) \rightarrow P'(4, -6)$

2. Calculate Distances for Corresponding Vertices
   Next, measure the vertical distance between the corresponding points:

   • For $M$ and $M'$,
     $$ \text{Distance } = |-8 - (-4)| = |-8 + 4| = 4 $$
   • For $N$ and $N'$,
     $$ \text{Distance } = |-8 - (-2)| = |-8 + 2| = 6 $$
   • For $O$ and $O'$,
     $$ \text{Distance } = |6 - 2| = 4 $$
   • For $P$ and $P'$,
     $$ \text{Distance } = |-6 - (-2)| = |-6 + 2| = 4 $$

3. Determine the Scale Factor
   The scale factor can be found by comparing any corresponding sides. We can use the distance between $M$ and $M'$ and between $N$ and $N'$. For example, using $M$ and $M'$:
   $$ \text{Scale Factor} = \frac{\text{Distance of M'}}{\text{Distance of M}} = \frac{4}{4} $$
   But for $M$ to $N$, we can use $M$ and $P$:
   $$ \text{Scale Factor} = \frac{6}{2} = 3 $$

4. Final Calculation
   The scale factor for the dilation from trapezoid $MNOP$ to trapezoid $M'N'O'P'$ is thus 3.