Collinear Points

Three or more points are collinear if they are part of the same straight line and as a result the rank of the vectors is 1.


Examples

1.Determine if the points A = (2, 3, 1), B = (5, 4, 3) and C = (2, 1, 2) are collinear.

Collinear Point Example

Collinear Point Example

Vector Rank

Vector Rank

The points are not collinear.


Midpoint

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

1.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


2.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 of 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