To find the area of triangle $\triangle JKL$, we can use the formula for the area of a triangle given three points in a coordinate plane:

$\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$

The coordinates of points $J$, $K$, and $L$ from the graph are approximately:

• $J(5, -10)$
• $K(4, 10)$
• $L(-6, 6)$

Let me calculate the area using these points.The area of triangle $\triangle JKL$ is $102$ square units.

Would you like a more detailed explanation of the steps or have any other questions?

Here are some related questions you might explore:

1. How do you find the length of each side of the triangle?
2. What is the perimeter of triangle $JKL$?
3. How can you determine if triangle $JKL$ is a right triangle using the distance formula?
4. What is the equation of the line passing through points $J$ and $K$?
5. Can the area of this triangle be calculated using Heron's formula?

Tip: In coordinate geometry, using absolute values in the area formula ensures that we get a positive area regardless of the order of the vertices.