Math Problem Statement

Solve part c

Given that O is the origin, find the area of the triangle OAB.

Solution

To solve part (c) of the problem, we need to find the area of triangle OABOAB, where OO is the origin. We need the coordinates of points AA and BB to use the formula for the area of a triangle with given vertices.

The formula for the area of a triangle with vertices O=(0,0)O = (0, 0), A=(x1,y1)A = (x_1, y_1), and B=(x2,y2)B = (x_2, y_2) is given by:

Area=12x1y2x2y1\text{Area} = \frac{1}{2} \left| x_1 y_2 - x_2 y_1 \right|

Please provide the coordinates of points AA and BB so I can calculate the area of the triangle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry

Formulas

Area of triangle with vertices O(x1, y1), A(x2, y2), B(x3, y3): Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Area of triangle with origin as vertex: Area = 1/2 * |x1 * y2 - x2 * y1|

Theorems

Area of triangle using determinants

Suitable Grade Level

Grades 9-12