Find the coordinates of the point that divides the line segment joining A(1, −2) and B(7, 4) internally in the ratio 2 : 1.

Find k if the distance between (2, −3) and (10, k) is 10 units.

Show that the points (1, 1), (4, 4) and (6, 6) are collinear using the distance formula.

Find the centroid of the triangle whose vertices are (1, 2), (3, −4) and (5, 8).

Find the ratio in which the x-axis divides the line segment joining (2, −3) and (5, 6).

Find the coordinates of the point that divides the join of (1, 2) and (7, 11) internally in the ratio 1 : 2.

The midpoint of the segment joining A(2, k) and B(6, 8) is (4, 5). Find k.