Midpoint

Midpoint questions involve working with two ordered (x,y) pairs and finding their midpoint. Use the midpoint formula:(x_M, y_M) = (x₁ + x₂)/2, (y₁ + y₂)/2), where (x_M, y_M) is the midpoint and the x and y values on the right side of the equation are from the ordered pairs of that midpoint.

Occasionally these questions might give the midpoint and one of the ordered pairs, in which case a student must use normal algebra on the above equation to find the missing pair. Each variable will need to be dealt with separately for that algebra to work (it cannot be done simultaneously).

Calculate the Midpoint from given graph

You may be asked to calculate the midpoints of two points on a line on a two-dimensional graph.

In order to do so, you would take two points from the line and use the formulas provided below to find the midpoints.

midpoint x = (x₁ + x₂) ÷ 2

midpoint y = (y₁ + y₂) ÷ 2

Midpoints – Practical Problems

You may also need to use the midpoint formula in practical problems, like those involving points on a map.

These questions are an example of a practical application of the midpoint formula, and knowing this will help you with coordinate geometry problems on the exam.