the trapezoid tuvw is a dilation of the trapezoid tuvw. what is the scale factor of the dilation? simplify…
the trapezoid tuvw is a dilation of the trapezoid tuvw. 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.
Answer
Answer:
5
Explanation:
Step1: Select corresponding sides
Let's consider the horizontal - side lengths. For example, the length of side $WT$ in trapezoid $TUVW$: The coordinates of $W(- 2,1)$ and $T(2,1)$, so $WT=\vert2 - (-2)\vert=4$. The length of side $W'T'$ in trapezoid $T'U'V'W'$: The coordinates of $W'(-10,1)$ and $T'(10,1)$, so $W'T'=\vert10-(-10)\vert = 20$.
Step2: Calculate scale factor
The scale factor $k$ of a dilation is given by the ratio of the length of a side in the dilated figure to the length of the corresponding side in the original figure. So $k=\frac{W'T'}{WT}=\frac{20}{4}=5$.