Question

If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y − 10 = 0, find the value of k.

Find the coordinates of the points which divide the line segment joining A(−2, 2) and B(2, 8) into four equal parts.

If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y – 10 = 0, then find the value of k.

In a society, there is a circular park having two gates. The gates are placed at points A(10, 20) and B(50, 50), as shown in the figure below. Two fountains are installed at points P and Q on AB such that AP = PQ = QB.