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 key points

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

Step2: Calculate scale factor

Use the ratio of coordinates of a dilated point to its original point. For point $Q$ and $Q'$:
$\text{Scale factor} = \frac{x_{Q'}}{x_Q} = \frac{-5}{-1} = 3$
Verify with point $P$: $\frac{x_{P'}}{x_P} = \frac{-10}{-2} = 3$, $\frac{y_{P'}}{y_P} = \frac{-5}{-1} = 3$

Answer:

$3$