Question

One more query!!!!!!


The ratio in which the line segment A(-2,-3) nd B (3,7) is divided by the y axis is????????

Answer 1

Let the Point on 'Y' axis which divides the line segment joining A {-2 , -3} and B {3 , 7} be : {0 , y}

Let the Point {0 , y} divides the line segment joining A {-2 , -3} and B {3 , 7} in the ratio -- A : 1

According to Section Formula, when a point divides a line segment joining (x₁ , y₁) and (x₂ , y₂) in the ratio m : n then the co-ordinates of that point will be :

$\frac{mx_2 + nx_1}{m + n} , \frac{my_2 + ny_1}{m + n}$

here m = A and n = 1 and x₂ = 3 and x₁ = -2

As x - coordinate is zero

⇒ $\frac{3A - 2}{A + 1} = 0$

⇒ 3A - 2 = 0

⇒ A = 2/3

⇒ The Given Line Segment Divides the y axis in the Ratio of 2 : 3

Quick Approach :

Line Formed by joining (x₁ , y₁) and (x₂ , y₂) is divided by y - axis in the ratio : -x₁/x₂ (because always the x coordinate of point which divides will be zero)

⇒ Ax₂ + x₁ = 0

⇒ A = -x₁/x₂

Here x₁ = -2 and x₂ = 3

⇒ A = 2/3