Question

triangle lmn is a dilation of the triangle lmn. what is the scale factor of the dilation?

Explanation:

Step1: Identify corresponding points

Original triangle points: $L(-1,1)$, $M(0,-1)$, $N(0,1)$
Dilated triangle points: $L'(-4,4)$, $M'(0,-4)$, $N'(0,4)$

Step2: Calculate scale factor

Take coordinates of $L$ and $L'$:
Scale factor $k = \frac{x'}{x} = \frac{-4}{-1} = 4$
Verify with $N$ and $N'$: $k = \frac{4}{1} = 4$

Answer:

$4$