The area of a triangle is 5 . Two of its vertices are A(2,1) and B(3,- 2). The third vertex C li

step 1 As C lies on the line, we have the line, Y equal to X plus C, X plus 3, and C lies on this line,

The area of a triangle is 5 . Two of its vertices are A(2,1)...

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Key Concepts

Triangle Area in Coordinate Geometry

This concept involves computing the area of a triangle using the coordinates of its vertices. Typically, one uses the determinant method or the shoelace formula, in which the area is given as half the absolute value of the determinant formed by the vertex coordinates. This approach is essential because it converts a geometric problem into an algebraic equation that can be manipulated to find unknown quantities.

Equation of a Line

In coordinate geometry, a line is often expressed in slope?intercept form (y = mx + b) where m is the slope and b is the y-intercept. This is fundamental when a point is known to lie on a specific line, as substituting the point's coordinates into the equation provides a constraint that helps determine unknown variables.

Solving Absolute Value Equations in Geometric Contexts

When finding an unknown vertex based on a specified area, the formula may involve the absolute value of an expression, leading to two possible equations. Solving these absolute value equations correctly is critical for ensuring all potential geometric positions of the vertex that satisfy the area condition are considered.

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