Midpoint of a Line Segment

Midpoint

Midpoint

Midpoint Formula

Midpoint in 3D

If A = (x1, y1, z1) and B = (x2, y2, z2) are the endpoints of a line segment, the midpoint of the line segment is given by:

Midpoint

Equation of a Midpoint in the Plane


Examples

Calculate the coordinates of the midpoint from the line segment AB.

Midpoint Example

Midpoint Calculations

Midpoint Solution

Calculate the coordinates of Point C in the line segment AC, knowing that the midpoint is B = (2, −2) and an endpoint is A = (−3, 1).

Midpoint Calculations


If M1 = (2, 1), M2 = (3, 3) and M3 = (6, 2) are the midpoints of the sides that make up a triangle, what are the coordinates of the vertices?

Midpoints of a TriangleMidpoint Calculations

x1 = 7 x5 = 7 x3 = −1

y1 = 4 y5 = 0 y3 = 3

A(7, 4)B(5, 0) C(−1, 2)


If the line segment AB with endpoints A = (1,3) and B = (7, 5) is divided into four equal parts, what are the coordinates of the points of division?

Line SegmentMidpoints of a Line Segment


Given the endpoints A = (3, −2, 5) and B = (3, 1, 7), find the coordinates of the midpoint of the line segment that they determine.

Midpoint Example


The coordinates of consecutive vertices of a parallelogram are A = (1, 0, 0) and B = (0, 1, 0). If the center coordinates of M are (0, 0, 1), find the coordinates for the vertices C and D.

Midpoint of a Plane

Collinear Point Example

Collinear Point Calculations

Collinear Point Calculations

Collinear Point Solution

Collinear Point Operations

Collinear Point Operations

Collinear Point Operations

Collinear Point Solutions





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