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

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

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)

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

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

If the vertices of a triangle are (1, -3), (4, p) and (-9, 7) and its area is 15 sq. units, find the value (s) of p.