# Math Blog

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### Distance of a Point from a Straight Line | Length of the Perpendicular

We will learn how to find the perpendicular distance of a point from a straight line. Prove that the length of the perpendicular from a point (x$$_{1}$$, y$$_{1}$$) to a line ax + by + c = 0 is

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### Number Words 100 to 1000 | Reading and Writing the Number in Words

We will learn how to read and write the numbers words 100 to 1000. Reading and writing the number in words from 100 to 199: Read one hundred five for 105 Read one hundred eighteen for 118

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### Position of a Point Relative to a Line | Position of a Point and a Straight Line

We will learn how to find the position of a point relative to a line and also the condition for two points to lie on the same or opposite side of a given straight line.

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### Identical Straight Lines | Slope-intercept form of a Line | Identical Lines

When the coefficients of two straight lines are proportional they are called identical straight lines. Let us assume, the straight lines a$$_{1}$$ x + b$$_{1}$$ y + c$$_{1}$$ = 0

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### Condition of Perpendicularity of Two Lines | Two Lines are Perpendicular

We will learn how to find the condition of perpendicularity of two lines. If two lines AB and CD of slopes m1 and m2 are perpendicular, then the angle between the lines θ is of 90°.

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### Equation of a Line Perpendicular to a Line | Slope of a Perpendicular Line

We will learn how to find the equation of a line perpendicular to a line. Prove that the equation of a line perpendicular to a given line ax + by + c = 0 is bx - ay + λ = 0, where λ is a constant.

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### Theorem on Properties of Triangle | p/sin P = q/sin Q = r/sin R = 2K

Proof the theorem on properties of triangle p/sin P = q/sin Q = r/sin R = 2K. Proof: Let O be the circum-centre and R the circum-radius of any triangle PQR. Let O be the circum-centre and R

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### Properties of Triangles | Semi-perimeter| Circum-circle|Circum-radius|In-radius

In trigonometry we will discuss about the different properties of triangles. We know any triangle has six parts, the three sides and the three angles are generally called the elements of the triangle.

### Tan Theta Equals 0 | General Solution of the Equation tan θ = 0 | tan θ = 0

How to find the general solution of the equation tan θ = 0? Prove that the general solution of tan θ = 0 is θ = nπ, n ∈ Z.

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### Cos Theta Equals 0 | General Solution of the Equation cos θ = 0 | cos θ = 0

How to find the general solution of the equation cos θ = 0? Prove that the general solution of cos θ = 0 is θ = (2n + 1) π/2, n ∈ Z

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### Sin Theta Equals 0 | General Solution of the Equation sin θ = 0 | sin θ = 0

How to find the general solution of the equation sin θ = 0? Prove that the general solution of sin θ = 0 is θ = nπ, n ∈ Z Solution:

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### tan x Minus Square Root of 3 Equals 0 | tan x - √3 = 0 | tan x = √3

We will discuss about the general solution of the equation tan x minus square root of 3 equals 0 (i.e., tan x - √3 = 0) or tan x equals square root of 3 (i.e., tan x = √3).

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### Square Root of 2 cos x Minus 1 Equals 0 | √2 cos x - 1 = 0 | cos x = 1/√2

We will discuss about the general solution of the equation square root of 2 cos x minus 1 equals 0 (i.e., √2 cos x - 1 = 0) or cos x equals 1 by square root of 2 (i.e., cos x = 1/√2).

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### 2 sin x Minus 1 Equals 0 | 2 sin x - 1 = 0 | sin x = ½ | General Solution

We will discuss about the general solution of the equation 2 sin x minus 1 equals 0 (i.e., 2 sin x - 1 = 0) or sin x equals half (i.e., sin x = ½).

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### Equation of a Straight Line in Normal Form | Find the Equation of the Line

We will learn how to find the equation of a straight line in normal form. The equation of the straight line upon which the length of the perpendicular from the origin is p and this perpendicular

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### Straight Line in Intercept Form | Intercept Form of a Straight Line | Examples

We will learn how to find the equation of a straight line in intercept form. The equation of a line which cuts off intercepts a and b respectively from the x and y axes is x/a + y/b = 1.

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### Equation of a Line Parallel to a Line | Equation of Straight Line | Examples

We will learn how to find the equation of a line parallel to a line. Prove that the equation of a line parallel to a given line ax + by + λ = 0, where λ is a constant. Let, ax + by + c = 0 (b ≠ 0)

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### Worksheet on Place Value and Face Value | Place Value of the Digit | Answers

We will practice the questions given in the worksheet on place value and face value. In place value and face value we need to identify the digit which is highlighted whether in hundreds place

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### Numbers from 100 to 199 | Specialties in the Numerals | Numerals of the Numbers

Learn the numerals of the numbers from 100 to 199.Every number is 1 more than the number just before it. We know the greatest two digit number is ninety nine. It is written as 99.

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### Order with Hundreds, Tens and Ones | Name the Number just Before

We will learn to order with hundreds, tens and ones and discover the pattern to find the missing numerals. The number just before 212 is 211.

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### Worksheet on Counting by Tens | Sequence of Counting Patterns | Answers

Practice the questions given in the worksheet on counting by tens. The questions are related to number patterns where the students need to skip the numbers and count by 10’s.

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### Condition of Parallelism of Lines | Parallelism of Two given Straight Lines

We will learn how to find the condition of parallelism of lines. If two lines of slopes m$$_{1}$$ and m$$_{2}$$ are parallel, then the angle θ between them is of 90°. Therefore, tan θ = tan 0° = 0

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### Angle between Two Straight Lines | Angle between Two Intersecting Lines

We will learn how to find the angle between two straight lines. The angle θ between the lines having slope m$$_{1}$$ and m$$_{2}$$ is given by tan θ = ± $$\frac{m_{2} - m_{1}}{1 + m_{1} m_{2}}$$

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### Concurrency of Three Lines | Point of intersection of Two Lines | Examples

We will learn how to find the condition of concurrency of three straight lines. Three straight lines are said to be concurrent if they passes through a point i.e., they meet at a point.

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### How to Tell the Time? | Analogue & Digital clock |Understand the Concept of Time

Learn to tell the time is a great activity to have fun for all the children. How to tell the time? To tell the time we need to see and understand by looking at the clock. Kids can enjoy practicing

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### What is the Time? | Enjoy the Rhyme | The Hands on the Clock

What is the time? Time have two hands. One hand is the longest hand and its called the minute hand and the other hand is the short hand and its called the hour hand.

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### Worksheet on Months and Days | Number of Days for each Month

Practice the questions given in the worksheet on months and days. The questions are related to the names of the months that come before& after and the number of days in each month.

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### Point of Intersection of Two Lines | Coordinates of the Point of Intersection

We will learn how to find the co-ordinates of the point of intersection of two lines. Let the equations of two intersecting straight lines be a$$_{1}$$ x + b$$_{1}$$y + c$$_{1}$$ = 0 and

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### Point-slope Form | Equation of a Straight Line | Symmetrical Form of a Line

The equation of a line in point-slope form we will learn how to find the equation of the straight line which is inclined at a given angle to the positive direction of x-axis in anticlockwise

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### Slope-intercept Form |Equation of a Straight Line|Slope-intercept Form of a Line

We will learn how to find the slope-intercept form of a line. The equation of a straight line with slope m and making an intercept b on y-axis is y = mx + b Let a line AB intersects the y-axis

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### Equation of a Line Parallel to y-axis |Find the Equation of y-axis|Straight Line

We will learn how to find the equation of y-axis and equation of a line parallel to y-axis. Let AB be a straight line parallel to y-axis at a distance a units from it.

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### Equation of a Line Parallel to x-axis |Find the Equation of x-axis|Straight Line

Let AB be a straight line parallel to x-axis at a distance b units from it. Then, clearly, all points on the line AB have the same ordinate b. Thus, AB can be considered as the locus of a point

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### Slope of a Line through Two Given Points | Slop of Two Parallel Lines are Equal

How to find the slope of a line through two given points? Let (x$$_{1}$$, y$$_{1}$$) and (x$$_{2}$$, y$$_{2}$$) be two given cartesian co-ordinates of the point A and B respectively referred

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### Slope of a Straight Line | Angle of Inclination of a Line | Solved Examples

What is slope of a straight line? The tangent value of any trigonometric angle that a straight line makes with the positive direction of the x-axis in anticlockwise direction is called the

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### Months and Days | Months in a Year | Months of the Year | Millennium

We will discuss about the months and days in a year. There are 12 months in a year. They are: January, February, March, April, May, June, July, August, September, October, November and December.

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### Straight line in Two-point Form | Equation of a line passing through two Points

We will learn how to find the equation of a straight line in two-point form or the equation of the straight line through two given points.

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### Collinearity of Three Points | Condition of Collinearity | Concept of Slope

We will find the condition of collinearity of three given points by using the concept of slope. Let P (x1, y1), Q (x2, y2) and R (x3, y3) are three given points. If the points P, Q and R

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### Straight Line | Represents a Straight Line | Equation of the Straight Line

A straight line is a curve such that every point on the line segment joining any two points on it lies on it. If a point moves on a plane in a given direction then its locus is called

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### Problems on Surds | Simplest form of Surd | Express the Surd | Rationalization

We will solve different types of problems on surds. 1. State whether the following are surds or not with reasons (i) √5 × √10 (ii) √8 × √6

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### Worksheet on Days of the Week | Fun with Days of the Week!

Practice the questions given in the worksheet on days of the week. We know, 7 days makes one week. Starting from the first day of the week, the names of different days of the week are:

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### Rules of Surds | Every Rational Number is not a Surd | Rationalization of Surds

Some of the important rules of surds are listed below. 1. Every rational number is not a surd. 2. Every irrational number is a surd.

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### Express of a Simple Quadratic Surd | Unlike Quadratic Surds | Rational Quantity

We will learn how to express of a simple quadratic surd. We cannot express a simple quadratic surd by the following ways:

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### Product of two unlike Quadratic Surds | Product of Surds|Multiplication of Surds

The product of two unlike quadratic surds cannot be rational. Suppose, let √p and √q be two unlike quadratic surds. We have to show that √p ∙ √q cannot be rational.

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### Properties of Surds | Simple Quadratic Surd | Represent Rational Numbers

We will discuss about the different properties of surds. If a and b are both rationals and √x and √y are both surds and a + √x = b + √y then a = b and x = y If a not equal to b, let us assume

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### Conjugate Surds | Complementary Surds | Binomial Quadratic Surds

The sum and difference of two simple quadratic surds are said to be conjugate surds to each other. Conjugate surds are also known as complementary surds.

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### Rationalization of Surds | Rationalizing the Denominator of the Surd

We will discuss about the rationalization of surds. When the denominator of an expression is a surd which can be reduced to an expression with rational denominator, this process

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### Division of Surds | Divide a given Surd by another Surd | Rationalizing Factor

In division of surds we need to divide a given surd by another surd the quotient is first expressed as a fraction. Then by rationalizing the denominator the required quotient

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### Multiplication of Surds | Product of Two or more Surds | Product of Surd-factors

In multiplication of surds we will learn how to find the product of two or more surds. Follow the following steps to find the multiplication of two or more surds. Step I: Express each surd

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### Addition and Subtraction of Surds | Sum or Difference of Surds | Examples

In addition and subtraction of surds we will learn how to find the sum or difference of two or more surds only when they are in the simplest form of like surds. Follow the following steps

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