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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.

It is given that the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5).

So, AB = AC $\Rightarrow$ AB² = AC²

Using distance formula, we have

$\Rightarrow$ ( 0 - 3 )² + (2 - p )² = ( 0 - p )² = ( 2 - 5 )²

$\Rightarrow$ 9 + 4 + p² - 4p = p² + 9

$\Rightarrow$ 4 - 4p = 0

$\Rightarrow$ p = 1

Hence, the value of p = 1.

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.