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Coordinate Geometry

Question

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Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.

Solution

Suppose the point P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3) in the ratio K : 1

Co-ordinates of the point,

$P = (\frac{6 K + 2}{K + 1}, \frac{- 3 K + 3}{K + 1})$

But the co-ordinates of point P are given as (4, m)

$\frac{6 K + 2}{K + 1} = 4 . . . . (i) \frac{- 3 K + 3}{K + 1} = m . . . . . (i i) 6 K + 2 = 4 K + 4 2 K = 2 K = 1 P u t t i n g K = 1 i n e q u . (2) \frac{- 3 (1) + 3}{1 + 1} = m ∴ m = 0 R a t i o i s 1 : 1 a n d m = 0 i . e P i s t h e m i d p o i n t o f A B$

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Coordinate Geometry

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.

Some More Questions From Coordinate Geometry Chapter

Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.

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