Mathematics is a branch that science. Countless scientists take into consideration mathematics a pure science, one that is equal components precision and also imagination. Collinear points is a fancy, yet a precise, means of describing point out in a line.

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Collinear point out Definition

Mathematicians usage words an extremely exactly. In Euclidean geometry, Collinear points room points the all lied in the very same line, even if it is they room close together, far apart, or form a ray, heat segment, or line. A small Latin helps: col + linear = collinear.


col way "together." our word college originates from the very same prefix. Linear way line.

The combination, collinear, means points with each other on a solitary line.

Collinear points in real Life

Anytime you have actually a collection of individual items in a solitary straight line, you have actually models of collinear points. Intend you have actually eggs in a carton; every egg in one heat is a upright point:


Students seated at a long cafeteria table are collinear. Football football player on the heat of scrimmage are collinear. Rings on a shower head curtain, plants in one heat in a garden, number on a ruler, moviegoers in a ticket line, and also commuters seated on a train are collinear.

For real-life instances to be good models of upright points, you require to have the ability to draw a right line through them. Think of the separation, personal, instance kernels on one row of one ear of corn.

Collinear foods items are uncovered all over the globe. In Japan, human being enjoy Dango; sweet tiny dumplings arranged 3 to 5 on a skewer.


Sosatie is a south African food of tiny cubes the lamb or mutton interspersed with dried apricots, red onions, and mixed peppers, all on skewers.

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

In all cases, the little bits the food are lined increase on a bamboo or lumber skewer, for this reason they space all clues on a single line. They are all collinear.

Non-Collinear Points

What is no a model of upright points? The angle marks roughly the curved edge of a protractor, for one thing. Neither room spirals, helixes, all five corners that a pentagon, or points on a globe.

Here room some instances of non-collinear points:


Non-collinear points room a set of point out that execute not lie on the same line. Photo a sushi role in front of you. Sticking through our example above, a second skewer of food sitting next to ours would certainly not have any type of points collinear through our skewer, since they space all on a various skewer or line.

Points have to lie top top the exact same line to have actually collinearity. If photo a best triangle v two points brand on two various sides points L and also R. If allude L on the hypotenuse and allude R ~ above the base, then allude L and suggest R room non-collinear.

Collinear clues in Geometry

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


Two sets of upright points show up around the diagonals in this geometric figure:


But friend can likewise find every these various other collinear points due to the fact that only two points identify a line:


Collinear points Examples

We will leave you through a side watch of a little street brazier for making skewered meat kebabs. Notice the foot cross and have a bottom brace, i m sorry creates 2 triangles to store the brazier stable. Can you discover at least 10 set of collinear points?


We are sure you observed sets prefer points A and also B, C and also D, and also points A - F - E - I - D, yet did you additionally pick up on ones choose CH,  HE,  EG, and GB?

The clues C - H - E and also E - I - D, which type two sides of a triangle (the bottom triangle) are also collinear.

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Look in ~ points H - E - G and also E - G - B. Each of these 3 points space collinear together well. Store looking; more sets of upright points are waiting to be found!

Coplanar Points

We now understand that collinear points, sometimes spelled "colinear" (just on L), space points that lie on a directly line. Yet what about coplanar points? In a three dimensional world, coplanar points space a collection of points that lie top top the same plane. Learn an ext about coplanar points.