Question

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

Answer 1

⭐GivEn⭐

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

✴️(x,0) is named as C

⭐ForMula UsEd⭐

section formula:

$( \frac{m1x2 + m2x1}{m1 + m2} , \frac{m1y2 + m2y1}{m1 + m2} )$

SoLutioN:

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1:2 is refer as m1:m2

m1=1

m2=2

X1=2

y1=3

X2=5

y2=-6

$c = (\frac{1)(5) + (2)(2)}{1 + 2} , \frac{(1)( - 6) + (2)(3)}{1 + 2} )$

$c = \frac{5 + 4}{3} , \frac{ - 6 + 6}{3}$

$c = ( \frac{9}{3} , \frac{0}{3} )$

$c = (3,0)$

C(x,0) =(3,0)

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Answer 2

ATQ, A point on the x-axis divides the line segment joining the points (2, 3) and (5 - 6) in the ratio 1 : 2.

The point on the x-axis will have the coordinates (x, 0). Let this point be named D. [D(x, 0)]

[The y coordinate has to be 0 for the point to lie on the x-axis]We can find out the coordinates by using the section formula, where

m₁ : m₂ = 1 : 2

$\sf \Longrightarrow D(x, 0) = \Bigg( \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2} , \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2} \Bigg)$

$\sf \Longrightarrow D(x, 0) = \Bigg( \dfrac{(1)(5) + (2)(2)}{1 + 2} , \dfrac{(1)(-6) + (2)(3)}{1 + 2} \Bigg)$

$\Longrightarrow \sf D(x, 0) = \Bigg( \dfrac{5 + 4}{3} , \dfrac{-6 + 6}{ \ \ 3} \Bigg)$

$\Longrightarrow \sf D(x, 0) = \bigg( \dfrac{9}{3} , \dfrac{0}{3} \bigg)$

$\Longrightarrow \sf D(x, 0) = \Big( 3 , 0 \Big)$

Final answer: (3, 0)