The points A \left(\right. x_{1} , y_{1} \left.\right) , B \left(\right. x_{2} , y_{2} \left.\right) and C \left(\right. x_{3} , y_{3} \left.\right) are the vertices of \Delta ABC. What are the coordinates of the centroid of the \Delta ABC ?

Engineering

Mathematics

Line of Greatest Slope

Question

The points

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

and

C (x_{3}, y_{3})

are the vertices of

Δ

ABC.
What are the coordinates of the centroid of the

Δ

ABC ?

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Vertices of

δ A B C

are

A (- 8, 4), B (- 6, 6)

and

C (- 3, 9)

∴

Area of

Δ A B C = \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]

\Rightarrow

Area of

Δ = \frac{1}{2} [- 8 (6 - 9) - 6 (9 - 4) - 3 (4 - 6)]

= \frac{1}{2} [- 8 (- 3) - 6 (5) - 3 (- 2)]

= \frac{1}{2} [24 - 30 + 6] = 0

Hence , the area of given triangle is zero.

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