Question

in what ratio is the line segment joining the point (2, - 4 )and( 3,8) form of a divided by the x axis also find the point of division​

Answer 1

Answer

The ratio is 1:2

and the point of division is (7/3 , 0)

$\bf\large\underline{Given}$

• The points are (2 , -4) and (3 , 8)

$\bf\large\underline{To \: Find}$

• The ratio in which X-axis divides the line
• The point of division

$\bf\large\underline{Solution}$

Let the point of dividend by X-axis of the line joining the points be (x , 0) and the ratio be m:n

Also let the points be A(2 , -4) and B(3 , 8)

$\sf \underline{Applying \ section\ formula :}$

$\sf\implies x = \dfrac{3m + 2n}{m+n} \longrightarrow (1)$

And

$\sf\implies 0 = \dfrac{8m - 4n}{m + n} \\\\ \sf\implies 8m - 4n = 0 \\\\ \sf\implies 8m = 4n \\\\ \sf\implies 2m = n \\\\ \sf\implies \dfrac{m}{n} = \dfrac{1}{2} \\\\ \sf\implies m:n = 1:2$

Putting the value of m and n in (1) we have :

$\sf\implies x = \dfrac{3\times 1 + 2\times 2}{1+2}\\\\ \sf\implies x = \dfrac{7}{3}$

Therefore , the point of division is 7/3