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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.

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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
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