Question

find the coordinates of the point on x axis which divides the line segment joinig the points (2,3) and (5,-6) in the ratio 1:2​

Answer 1

$\bf\huge\blue{\underline{\underline{ Question : }}}$

Find the coordinates of the point on x axis which divides the line segment joinig the points (2,3) and (5,-6) in the ratio 1:2

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• The line segment joining (2,−3) and (5,6) is divided by x-axis in the ratio 1:2.

★ To find,

• The point on X - axis.

★ Let,

The point on X - axis be P(x, y).

By using Section formula, we get the value of the point P.

$\boxed{\rm{\red{ P(x, y) =\Bigg( \cfrac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}} , \cfrac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}\Bigg) }}}$

• x1 = 2 ; y1 = -3
• x2 = 5 ; y2 = 6
• m1 = 1 ; m2 = 2

$\sf\:\implies P(x, y) = \Bigg( \cfrac{ 1(5)+2(2)}{1+2} , \cfrac{1(6)+2(-3)}{1+2} \Bigg)$

$\sf\:\implies P(x, y) = \Bigg( \cfrac{5+4}{3} , \cfrac{6-6}{3} \Bigg)$

$\sf\:\implies P(x, y) = \Bigg( \cancel{\cfrac{9}{3}} \: \: \: , \cfrac{0}{3} \Bigg)$

$\sf\:\implies P(x, y) = (3,0)$

$\underline{\boxed{\rm{\purple{\therefore The\:point\:is\:P(3,0)}}}}\:\orange{\bigstar}$