Advertisement

Co-ordinate Geometry Class 9th Mathematics Part Ii MHB Solution

Co-ordinate Geometry Class 9th Mathematics Part Ii MHB Solution
Practice Set 7.1
  1. State in which quadrant or on which axis do the following points lie. A(-3, 2), B(-5,…
  2. In which quadrant are the following points? i. whose both co-ordinates are positive.…
  3. Draw the co-ordinate system on a plane and plot the following points. L(-2, 4), M(5,…
Practice Set 7.2
  1. On a graph paper plot the points A (3,0), B(3,3), C(0,3). Join A, B and B, C. What is…
  2. Write the equation of the line parallel to the Y-axis at a distance of 7 units from it…
  3. Write the equation of the line parallel to the X-axis at a distance of 5 units from it…
  4. The point Q(-3, -2) lies on a line parallel to the Y-axis. Write the equation of the…
  5. Y-axis and line x = -4 are parallel lines. What is the distance between them?…
  6. Which of the equations given below have graphs parallel to the X-axis, and which ones…
  7. On a graph paper, plot the points A(2, 3), B(6, -1) and C(0, 5). If those points are…
  8. Draw the graphs of the following equations on the same system of co-ordinates. Write…
  9. x + y = 2 Draw the graphs of the equations given below
  10. 3x-y = 0 Draw the graphs of the equations given below
  11. 3x-y = 0 Draw the graphs of the equations given below
Problem Set 7
  1. What is the form of co-ordinates of a point on the X-axis? Choose the correct…
  2. Any point on the line y=x is of the form ..... Choose the correct alternative answer…
  3. What is the equation of the X-axis? Choose the correct alternative answer for the…
  4. In which quadrant does the point (-4, -3) lie? Choose the correct alternative answer…
  5. What is the nature of the line which includes the points (-5,5), (6,5), (-3,5), (0,5)?…
  6. Which of the points P (-1,1), Q (3,-4), R(1,-1), S (-2,-3), T (-4,4) lie in the fourth…
  7. Some points are shown in the figure 7.11 With the help of it answer the following…
  8. Without plotting the points on a graph, state in which quadrant or on which axis do the…
  9. Plot the following points on the one and the same co-ordinate system. A(1, 3), B(-3,…
  10. In the graph alongside, line LM is parallel to the Y-axis. (Fig. 7.12) i. What is the…
  11. How many lines are there which are parallel to X-axis and having a distance 5 units?…
  12. If ‘a’ is a real number, what is the distance between the Y-axis and the line x = a?…

Practice Set 7.1
Question 1.

State in which quadrant or on which axis do the following points lie.

A(-3, 2), B(-5, -2), K(3.5, 1.5),

D(2, 10), E(37, 35), F(15, -18),

G(3, -7), H(0, -5), M(12, 0),

N(0, 9), P(0, 2.5), Q(-7, -3)


Answer:

The x-y coordinate system is shown below:



The points are calculated as below:




Question 2.

In which quadrant are the following points?

i. whose both co-ordinates are positive.

ii. whose both co-ordinates are negative.

iii. whose x co-ordinate is positive, and the y co-ordinate is negative.

iv. whose x co-ordinate is negative and y co-ordinate is positive.


Answer:

According to co-ordinates Geometry,

i. In First Quadrant, both co-ordinates are positive.


ii.In Third Quadrant, both co-ordinates are negative.


iii.In Fourth Quadrant, x co-ordinate is positive and the y co-ordinate is negative.


iv.In second Quadrant, x co-ordinate is negative and y co-ordinate is positive.


The coordinate-system is shown below:




Question 3.

Draw the co-ordinate system on a plane and plot the following points.

L(-2, 4), M(5, 6), N(-3, -4), P(2, -3), Q(6, -5), S(7, 0), T(0, -5)


Answer:

The graph is shown below:



Steps for plotting the points:


• Draw X-axis and Y-axis on the plane.


• To find the point M(5,6) draw a line parallel to the Y-axis through the point on X axis which represents the number 5. Through the point on Y-axis which represents the number 6 draw a line parallel to the X-axis .


• The point of intersection of these two lines parallel to the Y and X-axis respectively, is the point M(5,6).


• In the same way, plot the point Q (6,-5),P(2,-3),L(-2,4) and N(-3,-4).


• and the point S(7,0) is lies on X-axis and the point T(0,-5) lies on Y-axis.




Practice Set 7.2
Question 1.

On a graph paper plot the points A (3,0), B(3,3), C(0,3). Join A, B and B, C. What is the figure formed?


Answer:

The graph is shown below:



Steps are given below:


• O is a centre of XY planes.


• Firstly we have drawn a point A(3,0) which is lies on x-axis and then,


• To find the point B(3,3) draw a line parallel to the Y-axis through the point on X axis which represents the number 3. Through the point on Y-axis which represents the number 3 draw a line parallel to the X-axis .


• And then draw a point C(0,3) is lies on y-axis and,


• Joining a points A,B,C and O then it is formed a SQUARE.



Question 2.

Write the equation of the line parallel to the Y-axis at a distance of 7 units from it to its left.


Answer:

The equation of line parallel to Y-axis is x = a

 a = -7 (because 7 units from left)


 x = -7 is required equation.



X-Values


Steps to draw:


• On a graph paper draw the X-axis and the Y-axis.


• Since it is given that x = -7, draw a line on the left of the Y-axis at a distance of 7 units from it and parallel to it.



Question 3.

Write the equation of the line parallel to the X-axis at a distance of 5 units from it and below the X-axis.


Answer:

The equation of line parallel to X-axis is y = a

 a = -5 (because 5 units below the x-axis)


 y = -5 is required equation.



Steps:


• On a graph paper draw the X-axis and the Y-axis.


• Since it is given that y = -5, draw a line below the X-axis at a distance of 5 units from it and parallel to it.



Question 4.

The point Q( -3, -2) lies on a line parallel to the Y-axis. Write the equation of the line and draw its graph.


Answer:

The equation of line parallel to y-axis is x = a

 x = -3


And the given point is Q(-3,-2)




Question 5.

Y-axis and line x = -4 are parallel lines. What is the distance between them?


Answer:

The equation of line parallel to Y-axis is x = a.

 x = -4


 a = -4


Since the distance between and the line is 4 units.


The graph is shown below:




Question 6.

Which of the equations given below have graphs parallel to the X-axis, and which ones have graphs parallel to the Y-axis?

i. x=3 ii. y – 2 = 0

iii. x + 6 = 0 iv. Y = -5


Answer:

i. x = 3


 x = a


The line is parallel to y-axis.


The figure is shown below:



ii. y-2 = 0


 y = 2


 y = a


The figure is shown below:



And the line is parallel to x-axis.


iii. x + 6 = 0


 x = -6


The figure is shown below:



And the line is parallel to y-axis.


iv. y = -5


 y = a


Then, the line is parallel to x-axis.


The figure is shown below:




Question 7.

On a graph paper, plot the points A(2, 3), B(6, -1) and C(0, 5). If those points are collinear then draw the line which includes them. Write the co-ordinates of the points at which the line intersects the X-axis and the Y-axis.


Answer:

The figure is shown below:



• Yes, given points are collinear.


• The line intersects the x-axis at point D(5,0) and the y-axis at point C(0,5).



Question 8.

Draw the graphs of the following equations on the same system of co-ordinates. Write the co-ordinates of their points of intersection.

x + 4 = 0

y - 1 = 0

2x + 3 = 0

3y - 15 = 0


Answer:

Given equation are


The figure is shown below:



• On a graph paper draw the X-axis and the Y-axis.


• Since it is given that x = -4 and x = -1.5, draw a line on the left of the Y-axis at a distance of 4 and 1.5 units from it and parallel to it.


• Since it is given that y = 1 and y = 5, draw a line above the X-axis at a distance of 1and 5 units from it and parallel to it.


• These lines, parallel to the two axes, are the graphs of the given equations.


• And these lines are intersects at the point A(-1.5,1), B(-4,1),C(-1.5,5) and D(-4,5).



Question 9.

Draw the graphs of the equations given below

x + y = 2


Answer:

x + y = 2

According to the equation,




• Firstly we have findout the point with the help of given equation.


• Then after plot a xy plane in a coordinate axis.


• The points A,B and C are collinear because all the points lies in the straight line.



Question 10.

Draw the graphs of the equations given below

3x-y = 0


Answer:

3x-y = 0

According to the given equation,


Now we have find out the points are




• On a graph paper draw the X-axis and the Y-axis.


• Then the points A,B and c are collinear because its lies in a straight line.



Question 11.

Draw the graphs of the equations given below

3x-y = 0


Answer:

2x + y = 1

According to the given equation,


Now we have find out the points are




• On a graph paper draw the X-axis and the Y-axis.


• Then the points A,B and c are collinear because its lies in a straight line.




Problem Set 7
Question 1.

Choose the correct alternative answer for the following questions.

What is the form of co-ordinates of a point on the X-axis?
A. (b,b)

B. (o,b)

C. (a,o)

D. (a,a)


Answer:

This is because the y co-ordinate point is zero.


Question 2.

Choose the correct alternative answer for the following questions.

Any point on the line y=x is of the form .....
A. (a,a)

B. (o,a)

C. (a,o)

D. (a,-a)


Answer:

 y = x


Y = a then x = a.


Question 3.

Choose the correct alternative answer for the following questions.

What is the equation of the X-axis?
A. x =0

B. y =0

C. x+y=0

D. x=y


Answer:

y = m × x + c


Where c is the intercept of the line on y-axis and m is the gradient of the line. Since intercept of x-axis on y-axis is zero, so c = 0. Gradient of x-axis is also zero because it makes an angle zero with itself. So m = tan(theta) = 0. Putting these values in the general equation we get,


y = 0 × x + 0


y = 0. Thus we get the equation for x-axis as y = 0.


Question 4.

Choose the correct alternative answer for the following questions.

In which quadrant does the point
(-4, -3) lie?
A. First

B. Second

C. Third

D. Fourth


Answer:

Since both the x & y coordinate are negative. Hence, it lies in the third quadrant.



Question 5.

Choose the correct alternative answer for the following questions.

What is the nature of the line which includes the points (-5,5), (6,5),
(-3,5), (0,5)?
A. Passes through the origin,

B. Parallel to Y-axis.

C. Parallel to X-axis

D. None of these


Answer:

All the points are shown below:



Question 6.

Choose the correct alternative answer for the following questions.

Which of the points P (-1,1), Q (3,-4), R(1,-1), S (-2,-3), T (-4,4) lie in the fourth quadrant?
A. P and T

B. Q and R

C. only S

D. P and R


Answer:

For a point to lie in the 4th quadrant, the x-coordinate should be positive & the y-coordinate should be negative.


As shown in the figure:



The figure is given below:



Question 7.

Some points are shown in the figure 7.11



With the help of it answer the following questions :

i. Write the co-ordinates of the points Q and R.

ii. Write the co-ordinates of the points T and M.

iii. Which point lies in the third quadrant?

iv. Which are the points whose x and y co-ordinates are equal?


Answer:

i. The co-ordinates of the points are Q(-2,2) and R(4,-1).

ii. The co-ordinates of the points are T(0,-1) and M(3,0).


iii. The point lies in the third quadrant is S(-3,-2).


iv. Q(-2,2) (both the co-ordinates are equal)



Question 8.

Without plotting the points on a graph, state in which quadrant or on which axis do the following point lie.

i. (5, -3) ii. (-7, -12)

iii. (-23, 4) iv. (-9, 5)

v. (0, -3) vi. (-6, 0)


Answer:

We should plot the points according to the coordinate system:




Question 9.

Plot the following points on the one and the same co-ordinate system.

A(1, 3), B(-3, -1), C(1, -4),

D(-2, 3), E(0, -8), F(1, 0)


Answer:

We plot according to the coordinate system:





Question 10.

In the graph alongside, line LM is parallel to the Y-axis. (Fig. 7.12)



i. What is the distance of line LM from the Y-axis?

ii. Write the co-ordinates of the points P, Q and R.

iii. What is the difference between the x co-ordinates of the points L and M?


Answer:

i.The distance of line LM from the Y-axis is 3.

ii.The co-ordinates of the points are P(3,2),Q(3,-1)and R(3,0).


iii. The difference between the x co-ordinates of the points L and M is 6.



Question 11.

How many lines are there which are parallel to X-axis and having a distance 5 units?


Answer:

Suppose the required linear equation of a line is y = mx + c

Since, the line is parallel to x-axis, so m = 0


Then equation of the line will be y = c


And this line passes through the point at a distance of 5 units below the x-axis i.e (-5,0)


Then the equation of line is y = -5.


And similarly,


And this line passes through the point at a distance of 5 units above the x-axis i.e (5,0)


Then the equation of line is y = 5.



Question 12.

If ‘a’ is a real number, what is the distance between the Y-axis and the line x = a?


Answer:

The distance is a unit, assuming a is an arbitrary constant, which it is, given that you stated it’s a real number.

This is because the y-axis is the same as the line x = 0, and so the difference between the two lines will be a−0 units, or simply a units.


PDF FILE TO YOUR EMAIL IMMEDIATELY PURCHASE NOTES & PAPER SOLUTION. @ Rs. 50/- each (GST extra)

SUBJECTS

HINDI ENTIRE PAPER SOLUTION

MARATHI PAPER SOLUTION

SSC MATHS I PAPER SOLUTION

SSC MATHS II PAPER SOLUTION

SSC SCIENCE I PAPER SOLUTION

SSC SCIENCE II PAPER SOLUTION

SSC ENGLISH PAPER SOLUTION

SSC & HSC ENGLISH WRITING SKILL

HSC ACCOUNTS NOTES

HSC OCM NOTES

HSC ECONOMICS NOTES

HSC SECRETARIAL PRACTICE NOTES

2019 Board Paper Solution

HSC ENGLISH SET A 2019 21st February, 2019

HSC ENGLISH SET B 2019 21st February, 2019

HSC ENGLISH SET C 2019 21st February, 2019

HSC ENGLISH SET D 2019 21st February, 2019

SECRETARIAL PRACTICE (S.P) 2019 25th February, 2019

HSC XII PHYSICS 2019 25th February, 2019

CHEMISTRY XII HSC SOLUTION 27th, February, 2019

OCM PAPER SOLUTION 2019 27th, February, 2019

HSC MATHS PAPER SOLUTION COMMERCE, 2nd March, 2019

HSC MATHS PAPER SOLUTION SCIENCE 2nd, March, 2019

SSC ENGLISH STD 10 5TH MARCH, 2019.

HSC XII ACCOUNTS 2019 6th March, 2019

HSC XII BIOLOGY 2019 6TH March, 2019

HSC XII ECONOMICS 9Th March 2019

SSC Maths I March 2019 Solution 10th Standard11th, March, 2019

SSC MATHS II MARCH 2019 SOLUTION 10TH STD.13th March, 2019

SSC SCIENCE I MARCH 2019 SOLUTION 10TH STD. 15th March, 2019.

SSC SCIENCE II MARCH 2019 SOLUTION 10TH STD. 18th March, 2019.

SSC SOCIAL SCIENCE I MARCH 2019 SOLUTION20th March, 2019

SSC SOCIAL SCIENCE II MARCH 2019 SOLUTION, 22nd March, 2019

XII CBSE - BOARD - MARCH - 2019 ENGLISH - QP + SOLUTIONS, 2nd March, 2019

HSC Maharashtra Board Papers 2020

(Std 12th English Medium)

HSC ECONOMICS MARCH 2020

HSC OCM MARCH 2020

HSC ACCOUNTS MARCH 2020

HSC S.P. MARCH 2020

HSC ENGLISH MARCH 2020

HSC HINDI MARCH 2020

HSC MARATHI MARCH 2020

HSC MATHS MARCH 2020


SSC Maharashtra Board Papers 2020

(Std 10th English Medium)

English MARCH 2020

HindI MARCH 2020

Hindi (Composite) MARCH 2020

Marathi MARCH 2020

Mathematics (Paper 1) MARCH 2020

Mathematics (Paper 2) MARCH 2020

Sanskrit MARCH 2020

Sanskrit (Composite) MARCH 2020

Science (Paper 1) MARCH 2020

Science (Paper 2)

Geography Model Set 1 2020-2021


MUST REMEMBER THINGS on the day of Exam

Are you prepared? for English Grammar in Board Exam.

Paper Presentation In Board Exam

How to Score Good Marks in SSC Board Exams

Tips To Score More Than 90% Marks In 12th Board Exam

How to write English exams?

How to prepare for board exam when less time is left

How to memorise what you learn for board exam

No. 1 Simple Hack, you can try out, in preparing for Board Exam

How to Study for CBSE Class 10 Board Exams Subject Wise Tips?

JEE Main 2020 Registration Process – Exam Pattern & Important Dates


NEET UG 2020 Registration Process Exam Pattern & Important Dates

How can One Prepare for two Competitive Exams at the same time?

8 Proven Tips to Handle Anxiety before Exams!

BUY FROM PLAY STORE

DOWNLOAD OUR APP

HOW TO PURCHASE OUR NOTES?

S.P. Important Questions For Board Exam 2022

O.C.M. Important Questions for Board Exam. 2022

Economics Important Questions for Board Exam 2022

Chemistry Important Question Bank for board exam 2022

Physics – Section I- Important Question Bank for Maharashtra Board HSC Examination

Physics – Section II – Science- Important Question Bank for Maharashtra Board HSC 2022 Examination

Important-formula



THANKS