Question

Find the coordinates of a point which divides the join of (1,3) and (2,-1) in the ratio 3:2 internally

Answer 1

Given ,

• The coordinates of a point which divides the join of (1,3) and (2,-1) in the ratio 3:2 internally

Let , The coordinate of point be P(x,y)

We know that ,

The coordinates of a point which divides the join of (x1, y1) and (x2,y2) in the ratio m : n internally is given by

$\boxed{ \sf{x = \frac{m x_{2} + nx_{1}}{m + n} \: \: , \: \: y = \frac{m y_{2} + ny_{1}}{m + n}}}$

Thus ,

$\sf \mapsto x = \frac{3(2) + 2(1)}{3 + 2} \: \: , \: \: y = \frac{3( - 1) + 2(3)}{3 + 2} \\ \\ \sf \mapsto x = \frac{8}{5} \: \: ,\: \: y = \frac{3}{5}$

Therefore ,

• The coordinate of required point is P(8/5 , 3/5)