Question

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

Answer 1

To Find :-

The coordinate of the point on x - axis which divided the line segment joining the points ( 2 , 3 ) and ( 5 , -6 ) in the ratio 1 : 2.

Solution :-

Given that, the point is on x - axis.

So, y coordinate of the point = 0

We can find the x coordinate of the point be using section formula.

According to section formula :-

$\bullet \bf \ x \ coordinate = \dfrac{mx_2+nx_1}{m+n} \\\\\bullet \ y \ coordinate = \dfrac{ny_2+ny_1}{m+n}$

Here :-

$\bullet \sf \ x_1 = 2 \\\\\bullet \ x_2 = 5 \\\\\bullet \ m = 1 \\\\\bullet \ n = 2$

x coordinate :-

$\longrightarrow \sf \dfrac{( 1 \times 5)+(2 \times 2)}{1+2} \\\\\longrightarrow \dfrac{5+4}{3} \\\\\longrightarrow \dfrac{9}{3} \\\\\longrightarrow 3$

Coordinates of the point = ( 3 , 0 )

Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

Given that, the point is on x - axis.

So, y coordinate of the point = 0

We can find the x coordinate of the point be using section formula.

According to section formula :-

x coordinate = mx²+nx¹/m+n

y coordinate = ny²+ny¹/ny¹

Here :-

x¹ =2 x² =5

∙ m=1

∙ n=2

x coordinate :-

⟶ (1×5)+(2×2)/1+2

⟶ 5+4/3

⟶ 9/3

⟶ 3

Coordinates of the point = ( 3 , 0 ) Ans.