Co-Ordinate Geometry

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Some Important Definition of Geometry

Difference between a rectangle and a square:
1.  Only opposite sides of a rectangle are equal unlike square which has all sides equal.

Difference between a rectangle and a rhombus:

1.  Each angle of rectangle is 90 degrees unlike rhombus where angles are not equal to 90 degrees.

Difference between a Parallelogram and a rhombus:
If all sides of parallelogram are equal but angles are not equal to 90 degrees, then this parallelogram is called a rhombus.

Difference between a Rhombus and a square (Rhombus and square have all sides equal) : 

1.  Each angle of square has to be 90 degrees unlike rhombus.

Difference between a rectangle & a Rhombus:
1. Each angle of rectangle has to be 90 degrees unlike rhombus.

2. Unlike rhombus only opposite sides of rectangle are equal.

A square is a parallelogram with right angles and equal sides. A square is a particular case of a rectangle and a rhombus simultaneously. So, it shows both the properties of rhombus and rectangle simultaneously.

Square can be differentiated from a rectangle and rhombus due to following properties.
1. Unlike rectangle square needs to have all its sides equal.

2. Unlike rhombus square needs to have all angles equal to 90 degree.

Difference between the circumcenter and a centroid of a triangle.
The circumcenter is a point that is equidistant from all three vertices so that a circle can be drawn that passes through three vertices. The circle circumscribes the triangle and the triangle is inscribed in the circle.

The centroid is the center of gravity of the triangle. It is the point where the three altitudes of the triangle intersect. If it is an acute triangle, the intersection will take place inside the triangle. If you cut a triangle from a piece of cardboard, the triangle would balance perfectly on the head of a pin place at the centroid.

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Trapezoid

A quadrangle which has only one of the two opposite sides as parallel is called a Trapezoid.

The other opposite sides need not be parallel. If both pair of opposite sides of a trapezoid are parallel then it becomes a parallelogram. The trapezoid does not follow the basic properties of a parallelogram.

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Parallelograms
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Definition of a Parallelogram
A parallelogram is a quadrilateral that has two pairs of parallel sides.

Any two opposite sides of a parallelogram are called bases, a distance between them is called a height.

   

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Formula

1.   Distance between two points,       d = √(x2-x1)2 + (y2-y1)2

2.   Coordinates of a mid-points, (xm , Ym),     xm  = (x1+x2)/2  ,      Ym  = (y1+y2)/2                         

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