line and angle

Point :- A point is a mark of location . It is represented by a dot made using by a sharp tip of the pencil on the paper .It has no length , breadth or thickness. It has just a position and only its location can be determined. 

Line Segment:- A line segment is a state path connecting two points it has a definite length but not breath and thickness it is the shortest distance between the two points.
RAY:- A ray is a line segment which has only one end point and can be extended endlessly in the other direction. Clearly a ray has no definite length , breadth and thickness.
Line:- A line is a line segment which can be extended endlessly on both the sides. A line “L” had length only it has no breath and thickness.
Plane:- A flat and smooth surface that extends infinitely in the all the directions is called plane. It has length and breadth but no thickness.
 Relationship between points and lines in a plane 
1. Infinite number of lines can be drawn passing through a given points in a plane.
2. There is exactly one line passing through two distinct point in a plane. 
  Pair of line
1. Intersecting lines
2. parallel lines
3. transversal 
  Angle 
An angle is a figure formed by two rays having a common initial point.
Type of angle
1. Acute angle 
2. Right angle
3. Obtuse angle 
4. Straight angle 
5. Reflex angle 
6. Complete angle.

In a competitive examination containing 24 questions 5 marks are awarded for every correct answer and -2 marks are awarded for every incorrect answer and zero marks for questions not attempted. Rahul attempts 8 correct and 16 incorrect answers. find its score.

Total number of questions = 24

 Marks for 1 correct answer = 5 

Number of correct answer = 8 

Total marks for 8 correct answer = 8 × 5 

       = 40

Marks for 1 incorrect answer = - 2 

Number of incorrect answer = 16 

Marks for 16 incorrect answer = 16 × (- 2) 

  = - 32

 Rahul final score 40 +( - 32 ) = 8

A cement company earns a profit of rs 8 per bag of white cement sold and a loss of rs 5 per bag of grey cement sold. (a) The company sells 3000 bags of white cement and 5000 bags of grey cement in a month. What is its profit or loss? (b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6400 bags?

 Profit is denoted by positive integer and loss is denoted by negative integer.

Profit earned  by selling 1 bag of white cement is = rs 8 

Loss incurred by selling 1 bag of grey cement = -5

 (a) Profit earned by selling 3000 bags of white cement = 8 × 3000 =rs 24000 

Loss incurred by selling 5000 bags of grey cement = -5 ×5000

 = - 25000 RS 

Total profit/loss earned = profit + loss 

=24000 +( - 25000)

= -1000 

therefore a loss of rs 1000 will be incurred by the company.

(B)

Loss incurred while selling 6400 bags of grey cement = - 5 × 6400 = - 32000

Let the number of the bags of white cements to be sold be X.

 Profit earned by selling X bags of white cement = 8 × X = 8 X

In condition of no profit no loss profit earned+ loss incurred=0

8 X + (- 32000 ) = 0

 8 X = 32 000 

x = 4000

 Therefore 4000 bags of white cement must be sold. 

Write five pairs of integers (a , b) such that a/b = -3. One such pair is (6,-2) = (-3).

 1 ( -6 , 2 ) Because -6/2 = -3

 2 ( 12 , -4 )

 3 ( -12 , 4 )

 4 ( -15 , 5 )

 5 ( 15 , -5 )

An elevator decends into a mind shaft at the rate of 6 metre per minute. if the decent starts from 10 m above the ground level, how long will it take to reach -350 m?

 Distance descended is  denoted by a negative  integer.

Initial height is = 10 m

Final depth = -350 m

Total distance to be descended by the elevator is = 10 -(- 350 ) = 360 m

Time taken by the elevator to descend 6m = 1 m  

Thus, the time taken by the elevator to descend 360 m 

= 360 / 6 

= 60 minute 

= 1 hour