Collinearity equation

Collinearity equation is a way of figuring out if three points are lined up straight like a dot-to-dot picture. When we draw dots on a paper, we can connect them with a line to create a shape. But sometimes we need to determine if these dots or points that we have in our math problems are in a straight line or not. That’s where collinearity equation comes into play.

We can use the formula y - y1 = m(x - x1) to find out if three points are aligned or not. The equation helps us find out how much the y value changes when the x value changes. It works like this:

Let’s say we have three points: (1,2), (3,6) and (5,10). We want to find out if these three points lie on a straight line or not.

- First, we pick any two points from the given points, let’s say (1,2) and (3,6), and plug them into the equation as (x1,y1) and (x2,y2).
- Then, we calculate the slope of the line that passes through these two points by using the formula: m = (y2 - y1) / (x2 - x1)
- With this slope value, we can determine the y value of the third point (5,10) by using the equation: y - y1 = m(x - x1)
- We plug in the values we know: (5,10) for (x,y), (1,2) for (x1,y1), and the slope we calculated for m.
- We then simplify the equation to see if the y value we get matches the y value of our third point. If it matches, then all three points are collinear or in simple words, they all sit on a straight line. If it does not match, then the points are not collinear.

So, collinearity equation helps us figure out if any three points are sitting on a straight line or not by using a simple formula and some basic math calculations.