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 $(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}, \frac{z_{1} + z_{2} + z_{3}}{3})$ .

Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of ΔABC.

(i) The median from A meets BC at D. Find the coordinates of point D.

(ii) Find the coordinates of the point P on AD such that AP: PD = 2:1

(iii) Find the coordinates of point Q and R on medians BE and CF respectively such that BQ: QE = 2:1 and CR: RF = 2:1.

(iv) What do you observe?

(v) If A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃) are the vertices of ΔABC, find the coordinates of the centroid of the triangle.

Show that the centroid of the triangle with vertices A(x1, y1, z1), B(x2, y2, z2) and C(x3, y3, z3) is
((x1+x2+x3)/3, (y1+y2+y3)/3, (z1+z2+z3)/3).

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Centroid of a Triangle

Standard X Mathematics

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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,
$x = \frac{x_{1} + x_{2} + x_{3}}{3}$
$y = \frac{y_{1} + y_{2} + y_{3}}{3}$