Area of triangle with vertices x1- y1-x2- y2 -x3- y3 is given by

The correct option is B ½[ x1(y2 y3) + x2(y3 y1) + x3(y1 y2)]½[ x1(y2 y3) + x2(y3 y1) + x3(y1 y2)] ...

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Standard X

Mathematics

Area of a Triangle

Area of trian...

Question

Area of triangle with vertices (x_1,y₁), (x_2,y₂) & (x_3,y₃) is given by _______.

½[ x₁(y₂+y₃) - x₂(y₃+y₁) - x₃(y₁+y₂)]

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½[ x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]

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½[ x₁(y₂-y₃) - x₂(y₃-y₁) + x₃(y₁-y₂)]

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½[ x₁(y₂-y₃) + x₂(y₃-y₁) - x₃(y₁-y₂)]

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Solution

The correct option is B ½[ x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]
½[ x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]

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Find the centroid of the triangle with vertices A $(x_{1}, y_{1})$ , B $(x_{2}, y_{2})$ and C $(x_{3}, y_{3})$ .

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Q. If

A (x_{1}, y_{1}), B (x_{2}, y_{2}), C (x_{3}, y_{3})

are the vertices of an equilateral triangle and

(x_{1} - 4)^{2} + (y_{1} - 5)^{2} = (x_{2} - 4)^{2} + (y_{2} - 5)^{2} = (x_{3} - 4)^{2} + (y_{3} - 5)^{2},

then the value of

(y_{1} + y_{2} + y_{3}) - (x_{1} + x_{2} + x_{3})

Q. If

A (x_{1}, y_{1}), B x_{2}, y_{2}), C (x_{3}, y_{3})

are the vertices of an equilateral triangle and

(x_{1} - 2)^{2} + (y_{1} - 3)^{2} = (x_{2} - 2)^{2} + (y_{2} - 3)^{2} = (x_{3} - 2)^{2} + (y_{3} - 3)^{2}

, then

Q. If three points

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

lie on the same line, prove that

\frac{y_{2} - y_{3}}{x_{2} x_{3}} + \frac{y_{3} - y_{1}}{x_{3} x_{1}} + \frac{y_{1} - y_{2}}{x_{1} x_{2}} = 0

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Area of triangle with vertices (x1, y1), (x2, y2) & (x3, y3) is given by _______.

The correct option is B ½[ x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]½[ x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]

Area of triangle with vertices (x_1,y₁), (x_2,y₂) & (x_3,y₃) is given by _______.

The correct option is B ½[ x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]
½[ x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]