RBSE Class 10 Maths Notes Chapter 7 Coordinate Geometry

These comprehensive RBSE Class 10 Maths Notes Chapter 7 Coordinate Geometry will give a brief overview of all the concepts.

RBSE Class 10 Maths Chapter 7 Notes Coordinate Geometry

Important Points

1. Coordinate Geometry – In this Geometry the position of a point is represented by specific numbers, which we call coordinates and different figures (lines, curves etc.) formed by them are represented by algebraic equations. Thus this branch of Geometry has developed by mixture of geometry and algebra. Therefore on account of the use of coordinates this branch of Mathematics is called Coordinate Geometry.

2. Cartesian Coordinates – Let XOX’ and YOY’ be two mutually perpendicular lines in any plane which intersect at the point O. These are called Coordinate axes and 0 is called the origin. XOX’ and YOY’ are mutually perpendicular, so XOX’ and YOY’ are called right angular axes and rectangular coordinate axes.

1. y-coordinate of each point lying on x-axis is 0.
2. x-coordinate of each point lying on y-axis is 0.
3. Signs of Coordinates in Quadrants – If the coordinates of any point p in the plane be (x, y), then

In first quadrant, x > 0, y > 0; Coordinates (+, +)
In second quadrant, x < 0, y > 0; Coordinates (-, +)
In third quadrant, x < 0, y < 0; Coordinates (-, -)
In fourth quadrant, x > 0, y < 0; Coordinates (+, -)

To be Remembered –
(i) If coordinates of any point P be (x, y), then we may write it P(x, y).
(ii) Abscissa x-coordinate of any point is the perpendicular distance of the point from y-axis.
(iii) Ordinate or y-coordinate of any point is the perpendicular distance of the point from x-axis.
(iv) The abscissa of any point is positive towards the right of y-axis and negative towards the left of y-axis.
(v) The ordinate of any point is positive above x-axis and negative below x-axis.
(vi) If y = 0, then the point lies on x-axis.
(vii) If x = 0, then the point lies on y-axis.
(viii) If x = 0, y = 0, then the point is the origin.

6. Distance between two points – The distance between two points P(x₁, y₁) and Q(x₂, y₂) lying in a plane
PQ =  \(\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \)

7. Particular Case – Distance of any point P (x, y) from origin (0, 0) OP \(\sqrt{x^{2}+y^{2}}\)

8. Internal Division of the Distance between Two Points –  Let A and B be any two points in a plane, if any point P has on line AB in between A and B. Then such a division is called Internal Division.

Let A(x₁, y₁) and B(x₂, y₂) be two points in a plane and the point P(.y, y) divides internally the line segment AB in the ratio m₁ : m₂, then the required coordinates of the point P will be
\(\left[\frac{m_{1} x_{2}+m_{2} \dot{x}_{1}}{m_{1}+m_{2}}, \frac{m_{1} y_{2}+m_{2} y_{1}}{m_{1}+m_{2}}\right]\)

9. If P divides the line segment AB in the ratio k : 1, the coordinates of the point P will be
\(\left(\frac{k x_{2}+x_{1}}{k+1}, \frac{k y_{2}+y_{1}}{k+1}\right)\)

10. If point P is the mid-point of the line segment AB, i.e. P divides this in the ratio 1:1, then the coordinates of P will be
\(\left(\frac{x_{2}+x_{1}}{2}, \frac{y_{2}+y_{1}}{2}\right)\)

11. The area of the triangle formed by the points (x₁, y₁), (x₂, y₂) and (x₃, y₃) is the numerical value of the expression
\(\frac{1}{2}\left[x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right]\)