A set of distance problems with detailed solutions are presented.

Problem 1: Find the distance between the points (2, 3) and (0, 6).

Detailed Solution.

Problem 2: Find the distance between point (-1, -3) and the midpoint of the line segment joining (2, 4) and (4, 6).

Problem 3: Find x so that the distance between the points (-2, -3) and (-3, x) is equal to 5.

Problem 4: Find x and y if (2, 5) is the midpoint of points (x, y) and (-5, 6).

Problem 5: Find the point (0, y) that is equidistant from (4, -9) and (0, -2).

Problem 6: Show that the triangle that has (0, 1), (2, 3) and (2, -1) as vertices is right isosceles.

Problem 7: Find the length of the hypotenuse of the right triangle whose vertices are given by the points (-2, 1), (1, 1) and (1, 2).

Problem 8: Find a relationship between x and y so that the distance between the points (x, y) and (-2, 4) is equal to 5.

Problem 9: Find a relationship between x and y so that (x, y) is equidistant from the two points (-3, 4) and (0, -3).

Problem 10: Find a relationship between x and y so that the triangle whose vertices are given by (x, y), (1, 1) and (5, 1) is a right triangle with the hypotenuse defined by the points (1, 1) and (5, 1).