CBSE Class 10 Maths Chapter 7 Coordinate Geometry Notes

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 = $\sqrt { { \left( { x }_{ 2 }-{ x }_{ 1 } \right) }^{ 2 }+{ \left( { y }_{ 2 }-{ y }_{ 1 } \right) }^{ 2 } }$
Note. If O is the origin, the distance of a point P(x, y) from the origin O(0, 0) is given by
OP = $\sqrt { { x }^{ 2 }+{ y }^{ 2 } }$

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 $\frac { m }{ n }$ : 1 or k : 1, The
co-ordinates of P can also be written as P(x,y) = $\frac { { kx }_{ 2 }+{ x }_{ 1 } }{ k+1 } ,\frac { { ky }_{ 2 }+{ y }_{ 1 } }{ k+1 }$

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 ∆ = $\frac { 1 }{ 2 } \left[ { x }_{ 1 }\left( { y }_{ 2 }-{ y }_{ 3 } \right) +{ x }_{ 2 }\left( { y }_{ 3 }-{ y }_{ 1 } \right) +{ x }_{ 3 }\left( { y }_{ 1 }-{ y }_{ 2 } \right) \right]$
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
$P=\left( \frac { { x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 } }{ 3 } ,\frac { { y }_{ 1 }+{ y }_{ 2 }+{ y }_{ 3 } }{ 3 } \right)$

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