The point which divides the line segment joining the points (8, – 9) and (2,3) in ratio 1:2 internally lies in the

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I quadrant

II quadrant

III quadrant

IV quadrant

answer is D.

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Detailed Solution

Let A

(x 1, y 1)

and B

(x 2, y 2)

be the two points, and P(x, y) is a point on the line segment joining A and B such that AP : BP =

m 1

m 2

, then point P is said to divide line segment AB internally in the ratio

m 1

m 2

Then, coordinates of point P are,

P (x, y) = m 1 x 2 + m 2 x 1 m 1 + m 2, m 1 y 2 + m 2 y 1 m 1 + m 2

The above formula is known as the section formula for internal division.
Given that, a point divides the line segment joining the points (8, – 9) and (2, 3) in ratio 1:2 internally.
Let us consider P (x, y) as the required point.
The line segment A (8, -9) and B (2, 3) are divided at point P in the ratio 1:2.
Here

m 1 = 1, m 2 = 2, (x 1, y 1) = (8, − 9)

and

(x 2, y 2) = (2, 3)

Let us substitute the above values in section formula.

P (x, y) = 1 × 2 + 2 × 8 1 + 2, 1 × 3 + 2 × − 9 1 + 2 P (x, y) = 2 + 16 3, 3 − 18 3 P (x, y) = 183, − 15 3 P (x, y) = (6, − 5)

Now, we need to find in which quadrant the point P(6, -5) lies.
Here abscissa is positive and ordinate is negative.
So, the point (6, - 5) lies in the IV quadrant.
The correct option is (4).

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