Question 7 (v)
Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.
(e) If $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

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Solution

Looking at the coordinates of P in earlier sections of this question, coordinates of centroid can be given as (x, y) where,
$x = \frac{x_{1} + x_{2} + x_{3}}{3}$
$y = \frac{y_{1} + y_{2} + y_{3}}{3}$

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Q. Question 3 (iv)
The points

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

are the vertices of

Δ

ABC. What are the coordinates of the centroid of the triangle ABC?

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

Show that the coordinates of the centroid of the triangle with vertices $A (x_{1}, y_{1}, z_{1})$ , $B (x_{2}, y_{2}, z_{2})$ and $C (x_{3}, y_{3}, z_{3})$ is $(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}, \frac{z_{1} + z_{2} + z_{3}}{3})$ .

Q. If

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

are the vertices of a triangle, then the equation

∣ ∣ ∣ ∣ \begin{matrix} x & y & 1 x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} x & y & 1 x_{1} & y_{1} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0

represents

The area of triangle with vertices $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ is:

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Question 7 (v) Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC. (e) If A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

Looking at the coordinates of P in earlier sections of this question, coordinates of centroid can be given as (x, y) where, x=x1+x2+x33 y=y1+y2+y33

Question 7 (v)
Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.
(e) If $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

Looking at the coordinates of P in earlier sections of this question, coordinates of centroid can be given as (x, y) where,
$x = \frac{x_{1} + x_{2} + x_{3}}{3}$
$y = \frac{y_{1} + y_{2} + y_{3}}{3}$