Question

The point which divides the line segment joining the points (8,-9)and (2,3) in ratio 1:2 internally lies in line a) 1quadrant b) 2quadrant c) 3quadrant d) 4quadrant

Answer 1

4th quadrant

The point which divides the line segment joining the points (8, - 9) and (2, 3) in ratio 1 : 2 internally has coordinates (6, - 5) which lies in the 4th quadrant.

Concept:

If a point (x, y) divides the line segment joining the points (x₁, y₁) and (x₂, y₂) into the ratio m : n internally, then

x = (nx₁ + mx₂) / (m + n) and

y = (ny₁ + my₂) / (m + n)

Step-by-step explanation:

The given two points are (8, - 9) and (2, 3).

Ratio is 1 : 2

If (x, y) be the coordinates of the required point, then

x = [2 × 8 + 1 × 2] / (1 + 2) = 6 and

y = [2 × (- 9) + 1 × 3] / (1 + 2) = - 5

So, the required point is (6, - 5) which lies in the 4th quadrant.

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