# Co-ordinate Geometry - Class 10 : Notes

Notes for coordinate geometry chapter of class 10 Mathematics. Dronstudy provides free comprehensive chapterwise class 10 Mathematics notes with proper images & diagram.

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**(1) The abscissa and ordinate of a given point are the distances of the point from y-axis and x-axis respectively.**

**(2) The coordinates of any point on x-axis are of the form (x,0).**

**(3) The coordinates of any point on y-axis are of the form (0,y).**

**(4) The distance between points and is given by,
**

**If and , then distance between these two point is given as follow:**

*For Example:*

Here, ,

, Â

Let O be the distance between two points and .

The distance between two point is given by

Â

Hence the distance between two points is 13 units.

**(5) Distance of a point from the origin is given byÂ **

** For Example:Â ** and is given then distance between them i.e. is calculated as follow:

**(6) The coordinates of the point which divides the join of points and internally in the ration m:n areÂ **

** For Example:Â **Find the coordinates of the point which is divided the line segment joining (-1,3) and (4,-7) internally in the ratio 3:4.

**Solution:Â**Let the end points of AB be A(-1, 3) and B(4, -7).

(, ) and (, )

Also, and

Let be the required point, then by section formula, we have ,

Â Â Â Â Â Â Â Â Â Â Â ,

Â Â Â Â Â Â Â Â Â Â Â ,

Â Â Â Â Â Â Â Â Â Â Â ,

Hence, the required point is

**(7) The coordinates of the mid-point of the line segment joining the points and are .
**

**and**

*For Example:Â*So mid-point of is .

**(8) The coordinates of the centroid of triangle formed by the points , and areÂ **

** For Example:Â **Find centroid of triangle whose vertices are , ,

**Solution:Â**We know that the coordinates of the centroid of a triangle whose angular points are , and are

So, the coordinates of the centroid of a triangle whose vertices are , and are

**(9) The are of triangle formed by the points , and isÂ ****Â ****Or,
**

**Find area of triangle whose vertices are , ,**

*For Example:Â***Solution:Â**Let , and be the given points

Area of

Â

**(10) If points , and are collinear, then
**

**Let , and be the given points.**

*For Example:Â*Three points are collinear if area enclosed by three points is zero.

Area of

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