Co-ordinate Geometry Class 9th Mathematics AP Board Solution

Class 9th Mathematics AP Board Solution

Exercise 5.1
Question 1.

In a locality, there is a main road along North-South direction. The map is given below. With the help of the picture answer the following questions.



(i) What is the 3rd object on the left side in street no. 3?

(ii) Find the name of the 2nd house which is in right side of street 2.

(iii) Locate the position of Mr. K’s house.

(iv) How do you describe the position of the post office?

(v) How do you describe the location of the hospital?


Answer:

(i) From the given figure, we can see that the 3rd object on the left side in street no. 3 is “Water Tank”.


(ii) From the given figure, the name of the 2nd house which is in right side of street 2 is “Mr. J’s” house.


(iii) From the figure given, we see that, Mr. K’s house is the 3rd house on the right of street 2 going while towards east direction.


(iv) From the given figure, we see that the 1st building on the right side of the street 4 while going towards east is the post office.


(v) From the given figure, we see that the 3rd building on the left side of street 4 while going in the easy direction is the hospital.




Exercise 5.2
Question 1.

Write the quadrant in which the following points lie?

i) (-2, 3)

ii) (5, -3)

iii) (4, 2)

iv) (-7, -6)

v) (0, 8)

vi) (3, 0)

vii) (-4, 0)

viii) (0, -6)


Answer:

From the figure given below, we can tell the quadrants of the given points.



(i) The point A(-2,3) lies in the II quadrant.


(ii)The point B(5,-3) lies in the IV quadrant.


(iii) The point C(4,2) lies in the I quadrant.


(iv) The point D(-7,-6) lies in the III quadrant.


(v) The point E(0,8) lies on the Y-axis.


(vi) The point F(3,0) lies on the X-axis.


(vii) The point G(-4,0) lies on the X-axis.


(viii) The point H(0,-6) lies on the Y-axis.



Question 2.

Write the abscissae and ordinates of the following points.

i) (4, -8)

ii) (-5, 3)

iii) (0, 0)

iv) (5, 0)

v) (0, -8)

Note : Plural of abscissa is abscissae.


Answer:

As we know, the abscissa of a point is its x co-odinate and ordinate of a point is its y co-ordinate {if a point≡(x,y)}.


So,


(i) For the point (4,-8) :


abscissa : 4


ordinate : -8


(ii) For the point (-5,3) :


abscissa : -5


ordinate : 3


(iii) For the point (0,0) :


abscissa : 0


ordinate : 0


(iv) For the point (5,0) :


abscissa : 5


ordinate : 0


(v) For the point (0,-8) :


abscissa : 0


ordinate : -8



Question 3.

Which of the following points lie on the axes? Also name the axis.

i) (-5, -8)

ii) (0, 13)

iii) (4, -2)

iv) (-2, 0)

v) (0, -8)

vi) (7, 0)

vii) (0, 0)


Answer:


From the figure above, The points which lie on axes are :


(ii) (0, 13) which lies on the Y-axis


(iv) (-2, 0) which lies on the X-axis


(v) (0, -8) which lies on the Y-axis


(vi) (7, 0) which lies on the X-axis


(vii)(0, 0) which lies on the on both the axis.



Question 4.

Write the following based on the graph.

i) The ordinate of L

ii) The ordinate of Q

iii) The point denoted by (-2, -2)

iv) The point denoted by (5, 4)

v) The abscissa of N

vi) The abscissa of M



Answer:

From the above figure we can say that,


(i) The ordinate of point L is -7.


(ii) The ordinate of point Q is 7.


(iii) The point denoted by (-2, -2) is R.


(iv) The point denoted by (5, 4) is P.


(v) The abscissa of point N is 4.


(vi) The abscissa of point M is -3.



Question 5.

State True or False and write correct statement.

i. In the Cartesian plane the horizontal line is called Y - axis.

ii. In the Cartesian plane, the vertical line is called Y - axis.

iii. The point which lies on both the axes is called origin.

iv. The point (2, -3) lies in the third quadrant.

v. (-5, -8) lies in the fourth quadrant.

vi. The point (-x, -y) lies in the first quadrant where x <0, y < 0.


Answer:

(i)The statement given is “False”.


⇒ CORRECT STATEMENT : In the Cartesian plane the horizontal line is called X - axis.


(ii) The statement given is “True”


(iii) The statement given is “True”


(iv) The statement given is “False”.


⇒ CORRECT STATEMENT : The point (2, -3) lies in the fourth quadrant.


(v) The statement given is “False”.


⇒ CORRECT STATEMENT : The point (-5, -8) lies in the second quadrant.


(vi) The statement given is “True”.



Question 6.

Plot the following ordered pairs on a graph sheet. What do you observe?

(1, 0), (3, 0), (-2, 0 ), (-5, 0), (0, 0), (5, 0), (-6, 0)


Answer:


The above all points lie on the X-axis.



Question 7.

Plot the following ordered pairs on a graph sheet. What do you observe?

(0, 1), (0, 3), (0, -2), (0, -5), (0, 0), (0, 5), (0, -6)


Answer:


The above all points lie on the Y-axis.


We also saw that a point common to both the axes was (0,0) which is the origin.




Exercise 5.3
Question 1.

Plot the following points in the Cartesian plane whose x, y co-ordinates are given.



Answer:




Question 2.

Are the positions of (5, -8) and (-8, 5) is same? Justify your answer.


Answer:


No, positions of (5, -8) and (-8, 5) is not same because (5, -8) lies in IV quadrant and (-8, 5) lies in II quadrant.



Question 3.

What can you say about the position of the points (1, 2), (1, 3), (1, -4), (1, 0), and(1, 8). Locate on a graph sheet.


Answer:

From the given points (1, 2), (1, 3), (1, -4), (1, 0), and(1, 8), we can say that all these points lie on a line parallel to Y-axis at a distance of 1 unit.




Question 4.

What can you say about the position of the points (5, 4), (8, 4), (3, 4), (0, 4),(-4, 4), (-2, 4)? Locate the points on a graph sheet and justify your answer.


Answer:

From the given points (5, 4), (8, 4), (3, 4), (0, 4),(-4, 4), (-2, 4), we can say that all these points lie on a line parallel to X-axis at a distance of 4 units.




Question 5.

Plot the points (0, 0),(0, 3), (3, 4), (4, 0) in graph sheet. Join the points with straight lines to make a rectangle. Find the area of the rectangle.


Answer:

Plotting the points :



Joining the lines to form a rectangle and finding its area :



Finding the area :


From the graph, we can see that,


L = AD = 4 units


B = ED = 3 units


Now, area of rectangle = L × B = 4 × 3 = 12 sq. unit.


∴ Area of rectangle BEDA = 12 sq. unit.



Question 6.

Plot the points (2, 3), (6, 3) and (4, 7) in a graph sheet. Join them to make it a triangle. Find the area of the triangle.


Answer:

Plotting the points :



Joining the points to form a triangle and finding its area :



Finding the area :


From the graph, we can see that,


H = 4 units


B = AB = 4 units


Area of the triangle =  × B × H


 × 4 × 4 = 8 sq. unit.


∴ Area of triangle CAB = 8 sq. unit.



Question 7.

Plot at least six points in a graph sheet, each having the sum of its coordinates equal to 5. {Hint : ( -2, 7) (1, 4) .............}


Answer:

The points whose sum of co-ordinates is equal to 5 are :


(2,3), (3,2), (0,5), (5,0), (1,4), (4,1).




Question 8.

Look at the graph. Write the coordinates of the points A, B, C, D, E, F, G, H, I, J, K, L,L, M, N, P, O and Q.



Answer:

From the graph, we can see that co-ordinates of the given points are :


Co-ordinates of point A are : (-3,4)


Co-ordinates of point B are : (0,5)


Co-ordinates of point C are : (3,4)


Co-ordinates of point D are : (2,4)


Co-ordinates of point E are : (2,0)


Co-ordinates of point F are : (3,0)


Co-ordinates of point G are : (3,-1)


Co-ordinates of point H are : (0,-1)


Co-ordinates of point I are : (-3,-1)


Co-ordinates of point J are : (-3,0)


Co-ordinates of point K are : (-2,0)


Co-ordinates of point L are : (-2,4)


Co-ordinates of point M are : (-1,0)


Co-ordinates of point N are : (-1,3)


Co-ordinates of point O are : (0,0)


Co-ordinates of point P are : (1,3)


Co-ordinates of point Q are : (1,0)



Question 9.

In a graph Sheet Plot each pair of points, join them by line segments

i. (2, 5), (4, 7)

ii. (-3, 5), (-1, 7)

iii. (-3, -4), (2, -4)

iv. (-3, -5), (2, -5)

v. (4, -2), (4, -3)

vi. (-2, 4), (-2, 3)

vii. (-2, 1), (-2, 0)

Now join the following pairs of points by straight line segments, in the same graph.

viii. (-3, 5), (-3, 4)

ix. (2, 5), (2, -4)

x. (2, -4), (4, -2)

xi. (2, -4), (4, -3)

xii. (4, -2), (4, 7)

xiii. (4, 7), (-1, 7)

xiv. (-3, 2), (2, 2)

Now you will get a surprise figure.

What is it?


Answer:

Plotting the first set of points and forming their line segments :


i. (2, 5), (4, 7) → A,B


ii. (-3, 5), (-1, 7) → C,D


iii. (-3, -4), (2, -4) → E,F


iv. (-3, -5), (2, -5) → G,H


v. (4, -2), (4, -3) → I,J


vi. (-2, 4), (-2, 3) → K,L


vii. (-2, 1), (-2, 0) → M,N



Plotting the second set of points and forming their line segments :


viii. (-3, 5), (-3, 4) → O,P


ix. (2, 5), (2, -4) → Q,R


x. (2, -4), (4, -2) →S,T


xi. (2, -4), (4, -3) → U,V


xii. (4, -2), (4, 7) → W,X


xiii. (4, 7), (-1, 7) →Y,Z


xiv. (-3, 2), (2, 2) → A1,B1



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

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 2021

O.C.M. Important Questions for Board Exam. 2021

Economics Important Questions for Board Exam 2021

Chemistry Important Question Bank for board exam 2021

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

Physics – Section II – Science- Important Question Bank for Maharashtra Board HSC 2021 Examination