Understand Pythagorean triples

In Geometry Tutoring we know that a natural number, n , is said to be the perfect square of the natural number, a, if n = a*a . In other words, we can say that a natural number is called a perfect square if it is the square of some other natural number. By the term square of a number, we mean that the product of a number multiplied by itself.
Then we have also learnt some properties of perfect squares. Adding to such list of properties, we will learn one important property of perfect squares here. This property of perfect squares is called the Pythagorean triples. Let’s define the term first.
Three natural numbers m, n, p are said to to form a Pythagorean triples if m  Ì‚2 + n  Ì‚2 = p  Ì‚2
The Pythagorean triples formula comes from the Phythagorean Theorem of right triangles in which the square of the length of hypotenuse is equal to the sum of the squares of the other two sides. In Pythagoras theorem, given a, b to be the two sides of a right triangle & h as the hypotenuse of the triangle, we have the relation h  Ì‚2 = a Ì‚2 + b Ì‚2. According to Pythagorean triples formula , if m is a natural  number greater than 1 , i.e., m>1, we can find a Pythagorean triples using the formula ,
( 2m , m  Ì‚2 – 1 , m  Ì‚2 +1 )
Lets take an example from Andhra Pradesh Board sample papers

Putting m = 4 , we get the Pythagorean triples as
2m = 2 * 4 = 8
m  Ì‚2 – 1 = 16 – 1 = 15
m  Ì‚2 + 1 = 16 + 1 = 17
Thus , the numbers 8, 15, 17 form the Pythagorean triples. For more information read here

This was all about Pythagorean triples. Visit our blogs for more information on Perpendicular Linesplanes and pythagorean theorem in grade vii

Coordinate geometry

In mathematics the coordinate geometry have a great importance. So we are going to discuss here the coordinate geometry. To understand the coordinate geometry you should be familiar with some related terms of coordinate geometry. The grid is a combination of horizontal (Find Horizontal Asymptote) and vertical lines that makes the squares. On the grid squares two points are there called axis, the x- axis and y- axis, the x axis represents the horizontal line and y axis represents the vertical lines. Both the points are intersecting on some point that is O point and called the origin. In which we determine the distance between the two points or the simple definition of the coordinate geometry is that, it is used mainly to address the point that are on the plane by using numbers of pairs that should be in ordered form.
Coordinate geometry formulas are used to define some coordinate geometry topics.
To determine the distance between the two pints we use distance formula that is
Distance d = √ [(x_{2 –} x₁)² + (y_{2 –} y₁)² ],
To find the angle between the two lines, we have formula θ tan – ¹m, where ‘m’ is slope, an angle may be anyone like right, acute, obtuse etc.
The slope formula is m = (y₂ – y₁) / (x₂ – x₁), we can also find the slope for perpendicular and parallel lines.
The midpoint formula (x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2),
We can also find the area and perimeter of a polygon in the field of geometry that is defined by the points. We can also transform the shapes in the coordinate geometry. It is used mostly in real life constructions.


In upcoming posts we will discuss about Rotations and Statistical experiments. Visit our website for information on CBSE previous years 11 physics