Question

the triangle opq is a dilation of the triangle opq. 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: Identify corresponding points

Original points: $O(-1,0)$, $P(-2,-1)$, $Q(-1,0)$; Dilated points: $O'(-10,0)$, $P'(-10,-5)$, $Q'(-5,0)$

Step2: Calculate scale factor

Use coordinates of $O$ and $O'$:
$\text{Scale factor} = \frac{\text{Coordinate of } O'}{\text{Coordinate of } O} = \frac{-10}{-1} = 5$
Verify with $P$ and $P'$: $\frac{-10}{-2} = 5$, $\frac{-5}{-1} = 5$

Answer:

$5$