Question

the square tuvw is a dilation of the square 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.

Explanation:

Step1: Find side - length of original square

The side - length of square $TUVW$ can be found by looking at the distance between two adjacent vertices. For example, the distance between $T(- 2,2)$ and $W(1,2)$. Using the distance formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, here $x_1=-2,y_1 = 2,x_2=1,y_2 = 2$, so $d=\sqrt{(1+2)^2+(2 - 2)^2}=3$.

Step2: Find side - length of dilated square

The side - length of square $T'U'V'W'$ can be found by looking at the distance between two adjacent vertices. For example, the distance between $T'(-6,10)$ and $W'(6,10)$. Using the distance formula, with $x_1=-6,y_1 = 10,x_2=6,y_2 = 10$, we get $d=\sqrt{(6 + 6)^2+(10 - 10)^2}=12$.

Step3: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the side - length of the dilated figure to the side - length of the original figure. So $k=\frac{\text{side - length of }T'U'V'W'}{\text{side - length of }TUVW}=\frac{12}{3}=4$.

Answer:

4