Question

Question 3 (ii)
The points $A(x_1,y_1),B(x_2,y_2)andC(x_3,y_3)$ are the vertices of $\Delta$ ABC.
Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ:QE = 2:1 and CR:RF = 2:1.

Answer 1

Let the coordinates of a point P be (x,y)
Given that, the point P(x,y), divide the line joining
$A(x_1,y_1)andD(\frac{x_2,y_3}{2},\frac{y_2+y_3}{2})$
in the ratio 2:1, then the coordinate of P.

$\equiv [\frac{2\left(\frac{x_2+x_3}{2}\right)+1.x_1}{2+1},\frac{2\left(\frac{y_2+y_3}{2}\right)+1.y_1}{2+1}][Byinternalsectionformula,coordinatesofthepointare\{\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2},\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}\}]\equiv (\frac{x_2+x_3+x_1}{3},\frac{y_2+y_3+y_1}{3})$
So, required coordinates of point $P\equiv (\frac{x_2+x_3+x_1}{3},\frac{y_2+y_3+y_1}{3})$