Question

15 points! What is the scale factor of the dilation?

Answer 1

Answer: $\frac{1}{2}$

Step-by-step explanation:

Use the formula for calculate the distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Calculate the distance AB. Substitute the coordinates into the formula. Then:

$d_{AB}=\sqrt{(8-0)^2+(8-(-7))^2}$

$d_{AB}=17$

Calculate the distance A'B'. Substitute the coordinates into the formula. Then:

$d_{A'B'}=\sqrt{(2-6)^2+(1-5-(-6))^2}$

$d_{A'B'}=\frac{17}{2}$

As you can see, the distance A'B' is the distance AB multiplied by 1/2. Therefore, this is the scale factor.