Question

The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the ______.

Options

• I quadrant

• II quadrant

• III quadrant

• IV quadrant

Answer 1

The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the IV quadrant.

Explanation:

If P(x, y) divides the line segment joining A(x₁, y₂) and B(x₂, y₂) internally in the ratio m : n,

Then x = `(mx_2 + nx_1)/(m + n)` and y = `(my_2 + ny_1)/(m + n)`

Given that,

x₁ = 7, y₁ = – 6,

x₂ = 3, y₂ = 4,

m = 1 and n = 2

∴ x = `(1(3) + 2(7))/(1 + 2)`, y = `(1(4) + 2(-6))/(1 + 2)`   ...[By section formula]

⇒ x = `(3 + 14)/3`, y = `(4 - 12)/3`

⇒ x = `17/3`, y = `-8/3`

So, (x, y) = `(17/3, -8/3)` lies in IV quadrant.    ...[Since, in quadrant, x-coordinate is positive and y-coordinate is negative]