A coordinate graph consists of a rectangular grid with two crossing lines called axes. The x-axis is the horizontal line and the y-axis is the vertical line. The axes intersect each other at the point (0,0) which is also called the origin.

Operations that can be done in Coordinate Geometry

If we are given the coordinates of some points we can:

- Calculate the distance between them
- Finding the midpoint, slope or equation of a line segment
- Determine if the given set of lines are parallel or perpendicular
- Finding the area or perimeter of a given polygon defined by the points..
- Define the equations of different geometric figures.

For 2 lines having equations:

a1x+b1y=c1

a2x+b2y=c2

Unique Solution (meet at a single point) = (a_{1} / a_{2}) ≠ (b_{1} / b_{2})

No solutions (does not meet) = (a_{1} / a_{2}) = (b_{1} / b_{2}) ≠ (c_{1} / c_{2})

Infinitely many solution (overlapping) = (a_{1} / a_{2}) = (b_{1} / b_{2}) = (c_{1} / c_{2})

No solutions (does not meet) = (a

Infinitely many solution (overlapping) = (a

Given below is a graph showing which coordinates are having what signs in different quadrants?

Example: Find the distance between two Points: A (2,3) and B(5,6)?

Using the above formula:

The answer comes out to be 3&redic;2.

m1:m2 are

Example .Find the co-ordinates of point Z, which divides the join of P (4, -5) and Q (6, 3) internally in the ratio 2 :5

Sol: Let the co-ordinates of point Z are (x, y).

Must Read Co-ordinate Geometry Articles

- Co-ordinate Geometry: Theory & Formulas
- Co-ordinate Geometry: Solved Examples

y - 0 = 4/3 (x + 4) ⇒ 3y = 4x +16.

(x/a) + (y/b) = 1

Example:

What is the relation between different set of given lines:

a) y = 3x + 1

b) y = -1/3 x + 2

c) 1/3y = x - 3

The gradients of the lines are 3, -1/3 and 3 respectively. Therefore (a) and (b) and perpendicular, (b) and (c) are perpendicular and (a) and (c) are parallel.

What is the relation between different set of given lines:

a) y = 3x + 1

b) y = -1/3 x + 2

c) 1/3y = x - 3

The gradients of the lines are 3, -1/3 and 3 respectively. Therefore (a) and (b) and perpendicular, (b) and (c) are perpendicular and (a) and (c) are parallel.