# The Centroid of a Triangle Abc is at the Point (1, 1, 1). If the Coordinates of a and B Are (3, –5, 7) and (–1, 7, –6) Respectively, Find the Coordinates of the Point C. - Mathematics

The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of and are (3, –5, 7) and (–1, 7, –6) respectively, find the coordinates of the point C.

#### Solution

Let G be the centroid of$∆$ABC.
Given: G$\equiv \left( 1, 1, 1 \right)$

Let C$\equiv \left( x, y, z \right)$

$\text{ Then }, 1 = \frac{3 - 1 + x}{3}$
$\Rightarrow 3 = 3 - 1 + x$
$\Rightarrow 3 = 2 + x \Rightarrow x = 1$
$\text{ and } 1 = \frac{- 5 + 7 + y}{3}$
$\Rightarrow 3 = 2 + y$
$\Rightarrow y = 1$
$\text{ and } 1 = \frac{7 - 6 + z}{3}$
$\Rightarrow 3 = 1 + z$
$\Rightarrow z = 2$

$\therefore C \equiv \left( 1, 1, 2 \right)$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 28 Introduction to three dimensional coordinate geometry
Exercise 28.3 | Q 12 | Page 20