We are given that triangle $XYZ$ maps to triangle $MNO$ under the transformation $(x, y) \rightarrow (12x, 12y)$. We are given that $XY = 6$ and we need to find the length of $MN$.

1. Problem Description

We are given that triangle $XYZ$ maps to triangle $MNO$ under the transformation $(x, y) \rightarrow (12x, 12y)$. We are given that $XY = 6$ and we need to find the length of $MN$.

2. Solution Steps

The transformation $(x, y) \rightarrow (12x, 12y)$ is a dilation by a factor of

1

2. This means that the length of each side of the new triangle $MNO$ is 12 times the length of the corresponding side of triangle $XYZ$.

Since $XY$ corresponds to $MN$, we have $MN = 12 \times XY$.

Since $XY = 6$, we have $MN = 12 \times 6 = 72$.

3. Final Answer

$MN = 72$