Question

If centroid of ∆ABC, with B=(-2,5), C=(1,2)
lie on the line 3x+4y= 7, then locus of A, is​

Answer 1

Step-by-step explanation:

We have,

$B\equiv(-2,5)\:\:\:\&\:\:\:C\equiv(1,2)$

$\tt\green{Let\:\:the\:\:coordinates\:\:of\:\:A\:\:be}\:\:\blue{(h,k)}$

Now,

Coordinates of centroid is given by

$\alpha \equiv \bigg( \frac{ - 2 + 1 + h}{3} \bigg) \: \: \: and \: \: \: \beta \equiv \bigg( \frac{5 + 2 + k}{3} \bigg)$

Since, the centroid lies on the line $\sf{3x+4y=7}$, so,

$3 \alpha + 4 \beta = 7$

$\implies \: 3 \bigg( \frac{ - 1 + h}{3} \bigg) + 4 \bigg( \frac{7 + k}{3} \bigg) = 7$

$\implies \: ( - 1 + h) + \frac{4(7 + k)}{3} = 7$

$\implies \: 3( - 1 + h) + 4(7 + k) = 21$

$\implies \: - 3 + 3h + 28 + 4k = 21$

$\implies \: 3h + 25 + 4k = 21$

$\implies \: 3h + 4k + 4 = 0$

So,

$\large{\sf{\red{ LOCUS\colon\:\:3x+4y+4=0} } }$