**Coordinate Geometry**

Contents

__Coordinate Geometry__

To locate the position of a point on a plane, we require a pair of coordinate axes. The distance of a point from the y-axis is called its x-coordinate, or abscissa. The distance of a point from the x-axis is called its y-coordinate, or ordinate. The coordinates of a point on the x-axis are of the form (x, 0), and of a point on the y-axis are of the form (0, y).

Coordinate geometry is used in creating maps. It is also used in creating digital images. It has huge application in the field of architecture, physics, engineering, navigation, seismology and art.

__Distance Formula__

The distance of a point P(

*x*,*y*) from the origin is √*x*2 +*y*2 .**Numerical**: Find the distance between the following pairs of points (2, 3), (4, 1)

**Solution**: here x1 =2, y1 = 3 , x2 = 4 & y2 =1

__Section Formula__

So, 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 are { (m1x2 + m2x1)/(m1 + m2 ) , (m1y2 + m2y1)/(m1 + m2 ) } .This is known as the

**section formula**.Refer ExamFear video lessons for Proof

The mid-point of the line segment joining the points P(

*x*1,*y*1) and Q(*x*2,*y*2) is [(x1+x2)/2 ,(y1+y2)/2]**Numerical**: Find the coordinates of the point which divides the line segment joining the points (4, – 3) and (8, 5) in the ratio 3 : 1 internally

**Solution**: Using section formula P(x, y) = { (m1x2 + m2x1)/(m1 + m2 ) , (m1y2 + m2y1)/(m1 + m2 ) }

We get P(x, y) = { (3*8 + 1*4 )/(3+1) , (3* 5 + 1 *-3)/(3+1) } = (7,3)

__Area of a Triangle__

Area of Δ ABC, with A(x1,y1) , B(x2, y2) & C(x3,y3) is the given by

**½ [ x1(y2-y3) + x2 (y3-y1 ) + x3 (y1-y2)]**

**Numerical**: Find the area of a triangle whose vertices are (1, –1), (– 4, 6) and (–3, –5).

**Solution**:

Area of Δ ABC, with A(x1,y1) , B(x2, y2) & C(x3,y3) is the given by

**½ [ x1(y2-y3) + x2 (y3-y1 ) + x3 (y1-y2)]**Using this, Area of Triangle is ½ [1*(6+5) + (-4)* (-5 + 1) + (-3)* (-1-6) ]

Or Area = ½ [11+ 16 + 21] = 24 square units.

**Also Read :**

### MATHS Revision Notes

Chapter:01 Real Numbers System

Chapter:02 Polynomials

Chapter:03 Pair of Linear Equations in Two Variables

Chapter:04 Quadratic Equation

Chapter:05 Arithemetic Progressions

Chapter:06 Triangles

Chapter:07 Coordinate Geometry

Chapter:08 Introduction to Trignometry

Chapter:09 Some Application Of Trignometry

Chapter:10 Circles

Chapter:11 Constructions

Chapter:12 Area Related to Cirles

Chapter:13 Surface Area Volume

Chapter:14 Stastistics

Chapter:15 Probability