# Collinear Points in Geometry (Definition & Examples)

## Collinear points definition

Mathematicians use words very exactly. In Euclidean geometry, **Collinear** points are points that all lie in the same line, whether they are close together, far apart, or form a ray, line segment, or line.

## Collinear points in real life

Anytime you have a series of individual items in a single straight line, you have models of collinear points. Suppose you have eggs in a carton; each egg in one row is a collinear point:

Students seated at a long cafeteria table are collinear. Football players on the line of scrimmage are collinear. Rings on a shower curtain, plants in one row in a garden, numbers on a ruler, moviegoers in a ticket line, and commuters seated on a train are collinear.

For real-life examples to be good models of collinear points, you need to be able to draw a straight line through them. Think of the individual kernels on one row of an ear of corn.

## Non-collinear points

What is not a model of collinear points? The angle marks around the curved edge of a protractor, for one thing. Neither are spirals, helixes, all five corners of a pentagon, or points on a globe.

Non-collinear points are a set of points that do not lie on the same line. Picture a sushi roll in front of you. A second skewer of food sitting next to ours would not have any points collinear with our skewer, since they are all on a different skewer or line.

Points must lie on the same line to have collinearity. If picture a right triangle with two points label on two different sides **points L **and **R**. If **point L** on the hypotenuse and **point R** on the base, then **point L** and **point R** are non-collinear

## Collinear points in geometry

Very often, collinear points appear in geometric figures such as quadrilaterals, triangles, parallelograms, and more. Take this kite with two diagonals intersecting at **Point S**:

Two sets of collinear points appear around the diagonals in this geometric figure:

**K−S−T****I−S−E**

But you can also find all these other collinear points since only two points determine a line:

**KS****ST****IS****SE****KI****IT****TE****EK**

## Collinear points examples

We will leave you with a side view of a little street brazier for making skewered meat kebabs. Notice the legs cross and have a bottom brace, which creates two triangles to keep the brazier stable. Can you find at least **10** sets of collinear points?

We are sure you saw sets like **points A **and **B**, **C**, and** D**, and **points A−F−E−I−D**, but did you also pick up on ones like **CH**, **HE**, **EG**, and **GB**?

The **points C−H−E** and **E−I−D**, which form two sides of a triangle (the bottom triangle) are also collinear.

Look at **points H−E−G** and **E−G−B**. Each of these three points are collinear as well. Keep looking; more sets of collinear points are waiting to be found!

## Coplanar points

We now know that collinear points, sometimes spelled "colinear" (just on L), are points that lie on a straight line. But what about coplanar points? In a three dimensional world, coplanar points are a set of points that lie on the same plane. Learn more about coplanar points.