Midpoint of points

The midpoint of two points is the point that is exactly halfway between them.

Importantly, this means that the and coordinates of the midpoint are the averages of the and coordinates of the two points respectively.

Finding the midpoint of two points

To find the midpoint of the two points, we can add up the x-coordinates of both points, divide by 2 to get the average x-coordinate, and do the same for the y-coordinates.

Or, use the formula:

We can also separate the formula into its and components ( and are the x and y coordinates of the midpoint respectively):

Find the midpoint of the points (2, 3) and (6, 7).

• Values we know:
• Substitute into the formula:
• Answer: (4, 5).

Find the midpoint of the points (-1, 4) and (3, -2).

• Values we know:
• Substitute into the formula:
• Answer: (1, 1).

Find the midpoint of the points (0, 0) and (5, 10).

• Values we know:
• Substitute into the formula:
• Answer: (2.5, 5).

Find the midpoint of the points (-4, -6) and (4, 6).

• Values we know:
• Substitute into the formula:
• Answer: (0, 0).

Finding one point given the other point and the midpoint

Find the point A, given that the midpoint between point A and point B (4, 8) is (6, 10).

• Values we know:
  • Midpoint
• Using the midpoint formula, we can set up two equations:
• Solving for :
• Solving for :
• Answer: Point A is (8, 12).

Find the point C, given that the midpoint between point C and point D (2, -4) is (5, 1).

• Values we know:
  • Midpoint
• Using the midpoint formula, we can set up two equations:
• Solving for :
• Solving for :
• Answer: Point C is (8, 6).