https://file.aiquickdraw.com/mathbot/file/1725675481528q90wmjlt.jpg

The image shows a triangle labeled \( \triangle ABC \) with vertices at \( A(2, 8) \), \( B(5, 5) \), and \( C(2, 2) \), and the task asks to find the area of the triangle.

To find the area of a triangle given the coordinates of its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\), we use the following formula:

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

Let's calculate this now. The coordinates of the vertices are:
- \( A(2, 8) \)
- \( B(5, 5) \)
- \( C(2, 2) \)

Substituting these values into the formula:The area of the triangle \( \triangle ABC \) with vertices at \( A(2, 8) \), \( B(5, 5) \), and \( C(2, 2) \) is \( 9 \) square units.

Would you like more details or have any further questions?

Here are some related questions to expand your understanding:
1. How can we verify the area of a triangle using the base and height method?
2. What is the formula for calculating the perimeter of a triangle?
3. How do you find the centroid of a triangle given its vertices?
4. Can you use this method for any type of triangle?
5. How do you calculate the area of a triangle on a non-Cartesian plane?

**Tip:** For any triangle in a coordinate plane, always double-check vertex coordinates when using area formulas to avoid sign errors.

This problem asks to find the area of triangle ABC with vertices at A(2,8), B(5,5), and C(2,2). The area is calculated using the formula for the area of a triangle based on vertex coordinates. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation