Points and lines tutoring

Tutor is the person who teaches the kids and this teaching section is the tutoring. Tutoring is an open source for the students to gain knowledge that is in online a point is nothing but the dot , it has no dimension or no width, it’s only a simple black dot. In geometry co ordinates of a point which shows the particular place in a segment for representation.Line has two end points is called segment. Line segment is denoted with a connected piece of line.line segments names  has two endpoints and it is named by its endpoints.

Points and Lines Tutoring:

Tutoring about the geometric points and lines we have to know the classification of a points and lines. points and lines classification are as follows.

Collinear points:
When three or more points lies on the same line is said to be collinear points.

Midpoint:
A halfway point where line segment divides into two equal parts are called midpoint.

Equidistant point:
A point which is said to be equidistant in a line segment where point is equal length from other points which are in congruent then the point is equidistant point.

Parallel line segment:
Two lines which does not touch each other are called parallel lines.

Perpendicular line segment:
Two line segment  that form a L shape are called perpendicular lines.

Problems in Points and Lines Tutoring:

Example 1:
Find the distance between the points A(6,3) and B (2,1).

Solution:
Let assume "d" be the distance between A and B.           (x1,y1)= (6,3), (x2,y2)= (2,1).

Then d (A, B) =`sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

= `sqrt((2-6)^2 +(1-3))^2)`

= `sqrt((-4)^2+(-2)^2)`

= `sqrt(16+4)`

=`sqrt20`
=2`sqrt5`

Example 2:
Find co-ordinate of the mid point of the line segment joining given points A(-5,3) and B(2,1)

Solution:
The required mid point is
Formul a   `((x_1+x_2)/2 ,(y_1+y_2)/2)` here,  (x1, y1) = (-5,3),(x2, y2) = (2,1)

=  `((-5+2)/(2))``((3+1)/(2)) `

=   `(-3/2) ` , ` (4/2)`

=    `(-3/2, 2)`

Example 3:
Find the slope of the lines given (8,-5) and (4,2)

Solution:
(x1,y1)= (8,-5), (x2,y2)= (4,2).
We know to find slope of line,m=` (y_2-y_1) /(x_2-x_1)`

=`(2+5)/(4-8)`

m =`7/-4`

Example 4:
Find the equation of the line having slope  3 and y-intercept 5.

Solution:
Applying the equation of the line is y = mx + c
Given,       m =3 ,c = 5
y =  3x +5

or  y = 3x+5
or  -3x+y-5 = 0
3x-y+5 = 0.

Introduction for division math facts

Division is essentially the opposite of multiplication. Division finds the quotient of two numbers, the dividend divided by the divisor. Any dividend divided by zero is undefined. For positive numbers, if the dividend is larger than the divisor, the quotient is greater than one; otherwise it is less than one (a similar rule applies for negative numbers). The quotient multiplied by the divisor always yields the dividend.

Division is neither commutative nor associative. As it is helpful to look at subtraction as addition, it is helpful to look at division as multiplication of the dividend times the reciprocal of the divisor, that is a ÷ b = a × 1⁄b. When written as a product, it obeys all the properties of multiplication. (Source: Wikipedia)

Definition and Steps for Division Math Facts:

Definition for division:

Division is defined as an arithmetic function, which is the opposed process of multiplication. From the process of division, the proportion or ratio of two numbers be capable of be calculated.

Otherwise, the process of decision how many periods of one number is included in a further one. Symbol of division is ‘/’ or ‘÷’.

If we divide a number by another number, then

Dividend = (Divisor * Quotient) + Remainder

Steps for division math facts:

Step1. Division of two integers by the related signs resolve be positive sign

a) Positive integer ÷ positive integer = positive integer

b) Negative integer ÷ negative integer = positive integer

Step2. Division of two integers by the unlike signs will be negative

a) Positive integer ÷ negative integer = negative integer

b) Negative integer ÷ positive integer = negative integer.              

Division Math Facts Example Problems and Practice Problem:

Example problem for division math facts:

1. Solve the following division

36 ÷ 6

Solution:

36 ÷ 6

= (6 * 6) ÷ 6

Answer: 6

2. Solve the following division,

32 ÷ 4

Solution:

32 ÷ 4

= (4 * 8) ÷ 4

Answer: 8

3. Solve the following division,

48 ÷ 8

Solution:

48 ÷ 8

= (6 * 8) ÷ 8

Answer: 6

Practice problem for division math facts:

1.      - 49 ÷ 7 = -7 (unlike sign)

2.      56 ÷ 7 = 8 (like sign)

3.      48 ÷ 12 = 4 (like sign)

4.      81 ÷ 9 = 9(like sign).

Learning subtraction of square roots

A square of a number a is a number x. therefore x2=a .A number x whose square is a. Every positive real number a has a unique positive square root, called the principal square root. Square root denoted by a radical sign as sqrt of a. For positive ax, the principal square root can also be written in exponent notation, as a1/2. We can undo a exponent with a radical, and a radical can undo a power. The “`sqrt(a)` “symbol is called the "radical “symbol..The line across the top is called the vinculum.

Subtracting Square Root Terms

Subtracting square roots

Subtracting square roots is combining like terms when we need to do that with algebraic expressions. The induces (a square roots index is 2 `root(2)(a)` , a cube roots index is 3  `root(3)(a)` , a 4th roots index is 4 `root(4)(a)` ,a 5th roots index is 5 `root(5)(a)` etc.) or the radicands (enclosed by parentheses after SQRT or the expression under the root sign) are the same.

Just as with "regular" numbers, square roots can be subtracted together. But you might not be able to simplify the subtraction all the way down to one number. Just as "you can't subtract apples and oranges", so also you cannot combine "unlike" radicals. To subtract radical terms together, they have to have the same radical part.

Simplifying Square-Root Terms

Simplify a square root, we take out anything that is a perfect square; that is, we take out front anything that has two copies of the same factor.

We can raise numbers to powers other than just 2; we can cube things, raise them to the fourth power, raise them to the 100th power, and so forth.

(ab)^2=a^2b^2  and`sqrt(ab)`   = `sqrt(a)``sqrt(b)` but we can’t write this subtraction of square root  `sqrt(a-b)`  = `sqrt(a)` - `sqrt(b)`

Example Problems on Subtracting Square Root

Example Problems

1. (4 * `sqrt(2)` ) - (5 * `sqrt(2)` ) + (12 * `sqrt(2)` )
Solution: Combine like
= (4 - 5 + 12) * `sqrt(2)`
Answer is 11 * `sqrt(2)`

2. (53 * `sqrt(5)` ) - (5 * `sqrt(5)` )
Solution: Combine like terms
(53 - 5) * `sqrt(5)`
= 48 * `sqrt(5)`

3. (40 * `sqrt(5)` ) - (48* `sqrt(5)` )
Solution: Combine like terms by subtracting the numerical coefficients.
(40 - 48) * `sqrt(5)`
= -8 *`sqrt(5)`
`sqrt(3x+1)`-( -`sqrt(2x-1)` )= 1    subtracting 2 square roots with variables
`sqrt(3x+1)` = 1 - `sqrt(2x-1)`
Take square both sides
3x + 1 = 1 - 2 `sqrt(2x-1)` + 2x-1
3x + 1 - 1 -2x + 1 = -2 `sqrt(2x-1)`
x+1 = -2 `sqrt(2x-1)`
take Square both sides again
x^2 + 2x + 1 = 4(2x -1)
x^2 + 2x + 1 = 8x -4
x^2 -6x + 5 = 0
(x-5)(x-1) = 0
x1 = 5, x^2 = 1