Question

A) 3,-4) B(-4,3) are the vertices of triangle ABC if centroid of this triangle moves on the line 3x-2y=4 then the locus of the vertex C is the line​

Answer 1

Answer:

$required \: locus \: \: \: \: \: \: \: \: \: is \: \: \: \: \: \: 3x - 2y = 13.$

Step-by-step explanation:

$let \: the \: third \: vertex \: be \: \: (x \: \: \: \: \: y). \\ \\ \frac{x + 3 - 4}{3} = \alpha \: \: \: \: \: \: \: \: \: \: \frac{ y - 4 + 3}{3} = \beta \\ \\ \\ \frac{x - 1}{3} = \alpha \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{y - 1}{3} = \beta \\ \\ 3( \frac{x - 1}{3} ) - 2( \frac{y - 1}{3} ) = 4 \\ \\ 3x - 3 - 2y + 2 = 12 \\ \\ 3x - 2y - 1 = 12 \\ \\ required \: locus \: \: \: \: \: \: \: \: \: is \: \: \: \: \: \: 3x - 2y = 13.$