Coordinate Geometry

Question

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A point P divides the line segment joining the points A(3,-5) and B(-4, 8) such that $\frac{AP}{PB} = \frac{K}{1}$ . If P lies on the line x + y = 0, then find the value of K.

Solution

Let the co-ordinates of point P be (x, y)

Then using the section formula co-ordinates of P are.

$x = \frac{- 4 k + 3}{k + 1} y = \frac{8 k - 5}{k + 1}$

Since P lies on x + y = 0

$∴ \frac{- 4 k + 3}{k + 1} + \frac{8 k - 5}{k + 1} = 0 \Rightarrow 4 k - 2 = 0 \Rightarrow k = \frac{2}{4} \Rightarrow k = \frac{1}{2} Hence the value of k = \frac{1}{2} .$

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Coordinate Geometry

A point P divides the line segment joining the points A(3,-5) and B(-4, 8) such that $\frac{AP}{PB} = \frac{K}{1}$ . If P lies on the line x + y = 0, then find the value of K.

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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For Daily Free Study Material Join wiredfaculty

Coordinate Geometry

A point P divides the line segment joining the points A(3,-5) and B(-4, 8) such that APPB = K1 . If P lies on the line x + y = 0, then find the value of K.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A point P divides the line segment joining the points A(3,-5) and B(-4, 8) such that $\frac{AP}{PB} = \frac{K}{1}$ . If P lies on the line x + y = 0, then find the value of K.