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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 )

( 3, 5 )

It is given that the point P divides AB in the ratio 2 : 1.

Using the section formula, the coordinates of the point P are

$(\frac{(1 x 1) + (2 x 4)}{2 + 1}, \frac{(1 x 3) + (2 x 6)}{2 + 1}) = (\frac{1 + 8}{3}, \frac{3 + 12}{3}) = (3, 5)$

Hence, the coordinates of the point P are (3,5).

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.