Coordinate Geometry Class 10 Notes Maths Chapter 7

November 16, 2021 by Suman

CBSE Class 10 Maths Notes Chapter 7 Coordinate Geometry

• Position of a point P in the Cartesian plane with respect to co-ordinate axes is represented by the ordered pair (x, y).
  
• The line X’OX is called the X-axis and YOY’ is called the Y-axis.
• The part of intersection of the X-axis and Y-axis is called the origin O and the co-ordinates of O are (0, 0).
• The perpendicular distance of a point P from the Y-axis is the ‘x’ co-ordinate and is called the abscissa.
• The perpendicular distance of a point P from the X-axis is the ‘y’ co-ordinate and is called the ordinate.
• Signs of abscissa and ordinate in different quadrants are as given in the diagram:
  
• Any point on the X-axis is of the form (x, 0).
• Any point on the Y-axis is of the form (0, y).
• The distance between two points P(x1, y1) and Q (x2, y2) is given by
  PQ = √(x₂−x₁)²+(y₂−y₁)²
  Note. If O is the origin, the distance of a point P(x, y) from the origin O(0, 0) is given by
  OP = √x²+y²

Section formula. The coordinates of the point which divides the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio m : n are:

The above formula is section formula. The ratio m: n can also be written as m/n : 1 or k : 1, The
co-ordinates of P can also be written as P(x,y) = kx₂+x₁ / k+1 , ky₂+y₁ / k+1

The mid-point of the line segment joining the points P(x1, y1) and Q(x2, y2) is

Here m : n = 1 :1.

Area of a Triangle. The area of a triangle formed by points A(x1 y1), B(x2, y2) and C(x3, y3) is given by | ∆ |,
where ∆ = 1/2[x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)]
where ∆ represents the absolute value.

• Three points are collinear if |A| = 0.
• If P is centroid of a triangle then the median divides it in the ratio 2 :1. Co-ordinates of P are given by
  P=(x₁+x₂+x₃ / 3 , y₁+y₂+y₃ / 3)

Area of a quadrilateral, ABCD = ar(∆ABC) + ar(∆ADC)