Find the area of a triangle formed by the points A(6, 2), B(4, 7) and C(7, -4) Option 1: 2.5 unit^2 Option 2: 3.2 unit^2 Option 3: 3.5 unit^2 Option 4: 4.0 unit^2

Answer: 3.5 unit^2. Solution: Area = 1/2, x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2), = 1/2, 6(7+4) + 4(-4-2) + 7(2-7), = 1/2, 66 - 24 - 35, = 7/2 = 3.5 sq units.

Geometry

Triangles

Medium

Find the area of a triangle formed by the points A(6, 2), B(4, 7) and C(7, -4)

2.5 unit^2

3.2 unit^2

3.5 unit^2

4.0 unit^2

✅ Correct Option: 3

Area $= \dfrac{1}{2}|x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)|$

$= \dfrac{1}{2}|6(7+4) + 4(-4-2) + 7(2-7)|$

$= \dfrac{1}{2}|66 - 24 - 35| = \dfrac{7}{2} = 3.5$ sq units.

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