Question

find the coordinates of the point which divides the join of (-1,7)and(4,-3)in the ratio2:3

Answer 1

The coordinates of the point are(1,-3)

Answer 2

Question :-

find the coordinates of the point which divides the join of (-1,7)and(4,-3)in the ratio2:3.

Given :-

• Given points are (-1, 7), (4, -3)

• Ratio = 2:3

To find :-

The coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2:3.

Using formula:-

$\longmapsto\tt\boxed{Section\:Formula=x=\dfrac{{m}_{1}{x}_{2}+{m}_{2}{x}_{1}}{{m}_{1}+{m}_{2}}\:\:,\:\:y=\dfrac{{m}_{1}{y}_{2}+{m}_{2}{y}_{1}}{{m}_{1}+{m}_{2}}}$

Solution :-

Given points :-

A = (-1, 7)

B = (4, 3)

Ratio — 2:3

$\tt Let\: coordinates\: of \:required\: point \:are\: (x, y)$

$\rm x=\dfrac{2\times 4+ 3\times -1}{2+3}\:\:,\:\:y=\dfrac{2\times -3+ 3\times 7}{2+3}$

$\rm x=\dfrac{8-3}{5}\:\:,\:\:y=\dfrac{-6+21}{5}$

$\rm x=\dfrac{5}{5}\:\:,\:\:y=\dfrac{15}{5}$

$\rm x=\cancel\dfrac{5}{5}\:\:,\:\:y=\cancel\dfrac{15}{5}$

$\rm x=1\:\:,\:\:y=3$

Therefore,

Coordinates of required point are (1, 3)