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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.

$Suppose the point A (\frac{24}{11}, y) divides the line segment joining points P (2, - 2) and Q (3, 7) in the ratio k : 1 Then, the co - ordinates of A are (\frac{3 k + 2}{k + 1}, \frac{7 k - 2}{k + 1}) But, the co - ordinates of A are given as (\frac{24}{11}, y) . \Rightarrow \frac{3 k + 2}{k + 1} = \frac{24}{11} \Rightarrow 33 k + 22 = 24 k + 24 \Rightarrow 9 k = 2 \Rightarrow k = \frac{2}{9} Hence, the ratio is 2 : 9 . Also, \frac{7 k - 2}{k + 1} = y \Rightarrow \frac{7 x \frac{2}{9} - 2}{\frac{2}{9} + 1} = y \Rightarrow y = \frac{\frac{14 - 18}{9}}{\frac{2 + 9}{9}} = \frac{- 4}{9} x \frac{9}{11} \Rightarrow y = - \frac{4}{11}$

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.