Question

Find the ratio in which the line segment joining the points A (3,-3) and B (-2,7) is divided by x axis find the oordinates of the point of division

Answer 1

Answer:

Solution:

Concept used:

The coordinates of the point which divides

the line segment joining$({x_1},{y_1})and({x_2},{y_2})$ is

$(\frac{m{x_2}+n{x_1}}{m+n},\frac{m{y_2}+n{y_1}}{m+n})$

Given points are(3,-3),(-2,7)

Let P be the point which divides the line segment joining the given points internally in the ratio m:n

Then by section formula

the coordinates of P is

$(\frac{m(-2)+n(3)}{m+n},\frac{m(7)+n(-3)}{m+n})\\\\(\frac{-2m+3n}{m+n},\frac{7m-3n}{m+n})$

since P lies on x axis, its coordinates will be 0

$\frac{7m-3n}{m+n}=0$

7m-3n=0

7m=3n

$\frac{m}{n}=\frac{3}{7}$

m:n=3:7

The coordinates of P is

$(\frac{3(-2)+7(3)}{3+7},0)\\\\(\frac{-6+21}{10},0)\\\\(\frac{15}{10},0)\\\\(\frac{3}{2},0)$