# Coordinate Geometry Class 10 Notes Maths: Chapter 7  ## Coordinate Geometry

1. 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
2. The coordinates of a point on the X-axis are always (x, 0) and on the Y-axis, are always (0, y).
3. The distance between two points, A(x1, y1) and B(x2, y2) is given by the formula : AB or | AB | =√((x2 – x1)2 + (y2-y1)2)
4. Distance of a point A(x, y) from the origin O(0, 0) is given by OA or | OA | =√(x2 + y2)
5. Section Formula : If C(x, y) divides the line joining A(x1, y1) and B(x2, y2) internally in the ratio m : n, then coordinates of C(x, y) are (x, y) =((mx2 + nx1)/(m+n),(my2 + ny1)/(m+n))
6. Mid-point : The coordinates of the mid-point C, of a line segment joining points A(x1, y1) and B(x2, y2) (when m = n) are given by :((x1 + x2)/2,(y1+y2)/2)
7. Centroid of a Triangle : The coordinates of the centroid O of a triangle whose vertices are A(x1, y1), B(x2, y2) and C(x3, y3), are given by : ((x1 + x2+ x3)/ 3 ,( y1 + y2+ y3)/3)
8. The equation of a line parallel to the X-axis is y=b and parallel to the Y-axis is x=a.
9. Area of a Triangle : The area of a triangle whose vertices are A(x1, y1), B(x2, y2) and C(x3, y3) is given by :
1/2 |x1( y2 – y3) + x2( y3 – y1) + x3( y1 – y2 )|
10. If the points A(x1, y1), B(x2, y2) and C(x3, y3) are collinear, then x1( y2 – y3) + x2( y3 – y1) + x3( y1 – y2) = 0.