## Eduwhere's Concept: Coordinate Geometry Important formulas

- Neha Gore
- last edited by Neha Gore

**Section Formula**

Section formula in Coordinate Geometry is used to find coordinates when say a point C divides a segment AB in the ratio p:q.

There are two parts of section formula:

**Section Formula for Internal division:**

### A segment that is divided in the ratio m:n, the coordinates of the point C will be calculated using this formula.

**C = {[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}**

Breaking it down further, the x coordinate is (mx2+nx1)/(m+n) and the y coordinate is (my2+ny1)/(m+n)

**Section Formula for External division:**

### When the point P lies on the external part of the segment, this formula is used to calculate the coordinates.

**C = P={[(mx2-nx1)/(m-n)],[(my2-ny1)/(m-n)]}**

Breaking it down further, the x coordinate is (mx2-nx1)/(m-n) and the y coordinate is (my2-ny1)/(m-n)

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**MidPoint Formula:**

For a point that lies exactly on the centre of the segment, the midpoint formula is used to find the coordinates.

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**P={(x1+x2)/2,(y1+y2)/2}**

Breaking it down further, the x-coordinate is (x1+x2)/2 and the y-coordinate is (y1+y2)/2

**Distance Formula:**

This formula is based on the Pythagorean theorem which is used to find the distance between any 2 points.

**AB=√[(x2-x1)²+(y2-y1)²]**