# Coordinate Geometry Class 10 Notes Maths: Chapter 7

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## Coordinate Geometry

**Abscissa and Ordinate :**From a given point, the abscissa and the ordinate are the respective distances from the X-axis and the Y-axis respectively- The coordinates of a point on the X-axis are always (x, 0) and on the Y-axis, are always (0, y).
- The distance between two points, A(x
_{1}, y_{1}) and B(x_{2}, y_{2}) is given by the formula : AB or | AB | =√((x_{2}– x_{1})2 + (y_{2}-y_{1})^{2}) - Distance of a point A(x, y) from the origin O(0, 0) is given by OA or | OA | =√(x
^{2}+ y^{2}) **Section Formula :**If C(x, y) divides the line joining A(x_{1}, y_{1}) and B(x_{2}, y_{2}) internally in the ratio m : n, then coordinates of C(x, y) are (x, y) =((mx_{2}+ nx_{1})/(m+n),(my_{2}+ ny_{1})/(m+n))**Mid-point :**The coordinates of the mid-point C, of a line segment joining points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) (when m = n) are given by :((x_{1}+ x_{2})/2,(y_{1}+y_{2})/2)**Centroid of a Triangle :**The coordinates of the centroid O of a triangle whose vertices are A(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}), are given by : ((x_{1}+ x_{2}+ x_{3})/ 3 ,( y_{1}+ y_{2}+ y_{3})/3)- The equation of a line parallel to the X-axis is y=b and parallel to the Y-axis is x=a.
- Area of a Triangle : The area of a triangle whose vertices are A(x
_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}) is given by :

1/2 |x_{1}( y_{2}– y_{3}) + x_{2}( y_{3}– y_{1}) + x_{3}( y_{1}– y_{2})| - If the points A(x
_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}) are collinear, then x_{1}( y_{2}– y_{3}) + x_{2}( y_{3}– y_{1}) + x_{3}( y_{1}– y_{2}) = 0.