QJEEM04Ma211e: JEE Main 2004 Mathematics - Class 11 JEEM04Ma211e Solution: Let A ( 2 , − 3 ) and B ( − 2 , 1 ) be vertices of a triangle A …

Question

Verified Solution • 2025–26 Session moderate

Let

A (2, - 3)

and

B (- 2, 1)

be vertices of a triangle

A B C

. If the centroid of this triangle moves on the line

2 x + 3 y = 1

, then the locus of the vertex

C

is the line :

Accepted Answer

Let the vertex

C

be

(h, k),

then the

centroid of

Δ A B C

is

(\frac{2 + (- 2) + h}{3}, \frac{- 3 + 1 + k}{3})

or

(\frac{h}{3}, \frac{- 2 + k}{3}) .

It lies on

2 x + 3 y = 1

\Rightarrow \frac{2 h}{3} - 2 + k = 1

\Rightarrow 2 h + 3 k = 9

∴

Locus of

C

is

2 x + 3 y = 9

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