The line segment joining the points A(3,2) and B(5,1) is divided at the point P in the ratio 1:2 and P lies on the line 3x-18y + k =0. Find the value of K.

Find the point on the x-axis which is equidistant from the points (5,4) and (-2,3). Also find the area of triangle formed by points.

Determine the ratio in which the straight line x-y-2=0 divides the line segment joining (3,-1) and (8,9).

Find the ratio in which (-3, q) divides the line segment joining the points (-5,-4) and (-2, 3). Find the value of q.

Prove that the points P(0,-1), Q(-2,3) R(6,7) and S(8,3) are the vertices of a rectangle PQRS.

Prove that the points (7,10) (-2,5) and (3, -4) are the vertices of an isosceles right triangle.

The vertices of triangle PQR are P(6,-2), Q(0,-6) and R(4,8). Find the coordinates of mid point of PQ, QR and PR.

Find the point on y axis which is equidistant from the point (5,-2) and (-3,2).

Find the ration in which (11,15) divides the line segment joining (15,5) and (9,20).

Prove that the diagonals of a rectangle PQRS with vertices P(2,-1), Q(5,1), R(5,6) and S(2,6) are equal and bisect each other.