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Coordinate Geometry

Short Answer Type

391.

If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.

Long Answer Type

392.

In what ratio does the point $(\frac{24}{11}, y)$ divides the line segment joining the points P(2, -2) and Q(3, 7)? Also find the value of y.

Multiple Choice Questions

393.

The coordinates of the point P dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1 are

( 2, 4 )
( 3, 5 )
( 4, 2 )
( 5, 3 )

394.

If the coordinates of the one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (-2, 5), then the coordinates of the other end of the diameter are:

( -6, 7)
( -6, -7)
( 6,7)
( -6, -7)

Short Answer Type

395.

If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5) then find the value of p.

Long Answer Type

396.
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.

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

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