Mathematics is a branch of science. Many scientists consider mathematics a pure science, one that is equal parts precision and imagination. **Collinear points** is a fancy, but a precise, way of describing points in a line.

- Collinear Points Definition
- Collinear Points in Real Life
- Collinear Points in Geometry
- Collinear Points in Geometry
- Collinear Points Examples

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. A little Latin helps: ** col + linear = collinear**.

The combination, *collinear*, means points together on a single line.

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.

Collinear foods are found all over the globe. In Japan, people enjoy Dango; sweet little dumplings arranged three to five on a skewer.

Sosatie is a South African dish of little cubes of lamb or mutton interspersed with dried apricots, red onions, and mixed peppers, all on skewers.

Frigărui, a Romanian kebab, is cubes of meat with bacon, onions, tomatoes, bell peppers, and mushrooms.

In all cases, the little bits of food are lined up on a bamboo or wood skewer, so they are all points on a single line. They are all collinear.

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.

Here are some examples of non-collinear points:

Non-collinear points are a set of points that do not lie on the same line. Picture a sushi roll in front of you. Sticking with our example above, 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.

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

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:

- $KS$
- $ST$
- $IS$
- $SE$
- $KI$
- $IT$
- $TE$
- $EK$

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!

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.

Instructor: **Malcolm M.**

Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

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