If the coordinates of the vertices of a triangle are (6,7) (4,-5) (x,2x) and its area is 3sq.cm find the value of x
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Solution:-
Area of the triangle = 3 sq cm
Area of the triangle = 1/2 {x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)}
1/2 {6(- 5 - 2x) + 4(2x - 7) + x(7 + 5)}
- 30 - 12x + 8x - 28 + 7x + 5x = 6
- 30 + 8x - 28 = 6
8x = 6 + 28 + 30
8x = 64
x = 8
Answer.
Area of the triangle = 3 sq cm
Area of the triangle = 1/2 {x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)}
1/2 {6(- 5 - 2x) + 4(2x - 7) + x(7 + 5)}
- 30 - 12x + 8x - 28 + 7x + 5x = 6
- 30 + 8x - 28 = 6
8x = 6 + 28 + 30
8x = 64
x = 8
Answer.
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