JEE MATHEMATICS MCQ: STRAIGHT LINES

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Application +4 | -1

Let

A\left( {2, - 3} \right)

and

B\left( { - 2,1} \right)

be vertices of a triangle

ABC

. If the centroid of this triangle moves on the line

2x + 3y = 1

, then the locus of the vertex

C

is the line

View answer and explanation

Correct option: A

2x + 3y = 9

Option A (

2x + 3y = 9

) is correct because the centroid's locus is used to find the locus of vertex C, resulting in the equation

2x + 3y = 9

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\left\{ {a{t_1}{t_2},\;a\left( {{t_1} + {t_2})\} ,\{ a{t_2}{t_3},a({t_2} + {t_3}} \right)} \right\},\;\left\{ {a{t_3}{t_1},\;a\left( {{t_3} + {t_1}} \right)} \right\}

y = 2\;x + 4

6x = 3y + 5

{x^2} + {y^2} + 2xy - 8ax - 8ay - 9{a^2} = 0

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x+3 y=7

\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0