Triangle $LMN$ is dilated by a scale factor of $\frac{1}{4}$ centered at the origin. We are asked to find the coordinates of the resulting triangle.

1. Problem Description

Triangle $LMN$ is dilated by a scale factor of $\frac{1}{4}$ centered at the origin. We are asked to find the coordinates of the resulting triangle.

2. Solution Steps

First, we need to find the coordinates of the vertices of the original triangle $LMN$ from the graph.

$L$ appears to be at $(-4, 8)$.

$M$ appears to be at $(6, 4)$.

$N$ appears to be at $(-8, 0)$.

Next, we will apply the dilation factor of $\frac{1}{4}$ to each coordinate of each vertex.

To dilate a point $(x, y)$ by a scale factor $k$ centered at the origin, the new point is $(kx, ky)$.

For $L(-4, 8)$, the new coordinates $L'$ are:

$L' = (\frac{1}{4} \times -4, \frac{1}{4} \times 8) = (-1, 2)$.

For $M(6, 4)$, the new coordinates $M'$ are:

$M' = (\frac{1}{4} \times 6, \frac{1}{4} \times 4) = (\frac{6}{4}, 1) = (\frac{3}{2}, 1) = (1.5, 1)$.

For $N(-8, 0)$, the new coordinates $N'$ are:

$N' = (\frac{1}{4} \times -8, \frac{1}{4} \times 0) = (-2, 0)$.

3. Final Answer

The coordinates of the resulting triangle are:

$L'(-1, 2)$

$M'(1.5, 1)$

$N'(-2, 0)$