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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.

Learn how to calculate the area of triangle JKL using the coordinate plane method. This problem covers essential concepts of coordinate geometry and provides a step-by-step calculation using the formula for the area of a triangle with given points. Suitable for high school students in Grades 9-12.

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