# Coordinate Geometry Class 10 Notes Maths Chapter 7

#### CHAPTER AT A GLANCE

1. Coordinate of a Point in XY- Plane

The perpendicular distance of x a point from they-axis is called its x-coordinate or abscissa. The perpendicular distance y of a point from the x-axis is called its y-coordinate or ordinate. The x and y taken together in order is called coordinate of a point denoted by (x, y). The coordinate of the points on x-axis are of the form (x, 0) and the points on they-axis are of the form (0,y). Coordinate of origin is (0, 0).

2. Sign-conventions in the XV-Plane

The x and y-axis divide the plane into four parts known as quadrants denoted by I, II, III and IV. The sign of x-and y-coordinate in each of the quadrant is shown below:

3. Distance Formula

The distance between any two points
P(x1, y1) and Q(x2, y2) in the plane is given by,

Also the distance of the point P(x1, y1) from the origin is

4. Section Formula

The coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio m1: m2

(ii) The coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) externally in the ratio, m1 : m2

(iii) If the ratio in which P divides AB is K : I, then the coordinates of the point P will be

5. Mid-point Formula
The coordinates of the mid point P of the line segment joining the points A(x1, y1) and B(x2, y2) is

6. Area of a Triangle
The area of MBC formed by the vertices A(x1,y1), B(x2, y2) and C(x3,y3) is given by

Note:
(i) Area of triangle= 1/2 x base x Altitude
(ii) Area of polygon can be calculated by dividing it into the triangular region.
(iii) If three points are collinear then area of the triangle formed by them is
zero.

Related Articles: