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To find the area of triangle IJK with vertices at \(I(-5, -9)\), \(J(-2, -2)\), and \(K(-8, -4)\), we can use the formula for the area of a triangle given by coordinates:

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

Plugging in the coordinates of \(I\), \(J\), and \(K\):

\[
x_1 = -5, \, y_1 = -9; \, x_2 = -2, \, y_2 = -2; \, x_3 = -8, \, y_3 = -4
\]

\[
\text{Area} = \frac{1}{2} \left| (-5)(-2 + 4) + (-2)(-4 + 9) + (-8)(-9 + 2) \right|
\]

\[
\text{Area} = \frac{1}{2} \left| (-5)(2) + (-2)(5) + (-8)(-7) \right|
\]

\[
\text{Area} = \frac{1}{2} \left| -10 - 10 + 56 \right|
\]

\[
\text{Area} = \frac{1}{2} \left| 36 \right|
\]

\[
\text{Area} = 18 \text{ square units}
\]

Thus, the area of triangle IJK is 18 square units.

Would you like to delve into any details or do you have further questions on this solution? Here are some related questions to consider:

1. How do you find the perimeter of triangle IJK?
2. What is the length of each side of triangle IJK?
3. How can you confirm if triangle IJK is a right triangle?
4. What is the slope of each side of triangle IJK?
5. Can you calculate the coordinates of the centroid of triangle IJK?

Tip: When solving geometry problems involving coordinates, it can be helpful to sketch the points on graph paper to visualize relationships and distances.

What is the area, in square units, of triangle IJK with vertices I(-5,-9), J(-2,-2), and K(-8,-4)?

Learn how to calculate the area of a triangle with vertices at I(-5, -9), J(-2, -2), and K(-8, -4) using coordinate geometry. This solution involves applying the triangle area formula to find the area of 18 square units. Suitable for students in Grades 8-10.

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