The image shows a triangle $\triangle MLK$ with points $M$, $L$, and $K$ located at coordinates approximately:

• $M(-3, 1)$
• $L(2, 1)$
• $K(1, -2)$

The task is to dilate this figure by a factor of 4 centered at the origin.

To perform a dilation:

Given that the dilation is centered at the origin with a scale factor of 4, the coordinates of each point will be multiplied by 4. The new coordinates for each point after dilation are calculated as follows:

1. Point M: $(-3, 1) \rightarrow (-3 \times 4, 1 \times 4) = (-12, 4)$

2. Point L: $(2, 1) \rightarrow (2 \times 4, 1 \times 4) = (8, 4)$

3. Point K: $(1, -2) \rightarrow (1 \times 4, -2 \times 4) = (4, -8)$

The new triangle $\triangle M'L'K'$ has vertices:

• $M'(-12, 4)$
• $L'(8, 4)$
• $K'(4, -8)$

To complete the transformation, you can plot these new points on the graph.

Would you like further assistance or clarification on any step? Here are a few additional related questions to explore:

1. How would the triangle change if the dilation factor were negative?
2. What is the effect of dilating the triangle around a different center, say $(2, 2)$?
3. How does the area of the triangle change after dilation by a factor of 4?
4. Can you calculate the distances between the original and dilated points?
5. What would the result be if the dilation factor were $\frac{1}{2}$?

Tip: When dilating figures on a coordinate plane, always multiply both the x and y coordinates by the scale factor!