Geometry Midpoint Formula

Midpoint

Definition

• The midpoint of a line segment is the point that divides the segment into two equal parts.
• It is the point that is equidistant from both endpoints of the segment.

Midpoint Formula

• The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found using the formula:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

• Where M is the midpoint.

Properties

• The midpoint is the average of the x-coordinates and the average of the y-coordinates of the endpoints.
• The midpoint is the point of symmetry for the line segment.

Example

• Find the midpoint of the line segment with endpoints (3, 4) and (7, 10):

M = ((3 + 7) / 2, (4 + 10) / 2) = (5, 7)

Applications

• Midpoints are used in geometry to find the center of a triangle or a circle.
• Midpoints are used in engineering to find the center of gravity of an object.
• Midpoints are used in computer graphics to perform transformations and rotations.

Midpoint Definition

• Midpoint divides a line segment into two equal parts.
• It is equidistant from both endpoints of the segment.

Midpoint Formula

• Formula to find midpoint: M = ((x1 + x2) / 2, (y1 + y2) / 2).
• M represents the midpoint.
• x1 and x2 are x-coordinates of endpoints.
• y1 and y2 are y-coordinates of endpoints.

Midpoint Properties

• Midpoint is the average of x-coordinates and y-coordinates of endpoints.
• Midpoint is the point of symmetry for the line segment.

Example and Applications

• Example: Midpoint of (3, 4) and (7, 10) is (5, 7).
• Midpoints are used in geometry to find center of a triangle or a circle.
• Midpoints are used in engineering to find center of gravity of an object.
• Midpoints are used in computer graphics to perform transformations and rotations.

Learn about the definition and properties of midpoints in geometry, including the midpoint formula for finding the midpoint of a line segment.