EXERCISE 2.5.4
1. Fix up your own coordinate system on a graph paper and locate the following
points on the sheet
1 p(-3,5)
2 Q(0,-8)
3
4 S(-4,-9)
R(4,0)
--8
--7
(-3,5)
--6
--5
- -4
--3
--2
--1
-9 -8 -7 -6 -5 -4 -3 -2 -1
(4,0)
1
- -1
- -2
- -3
- -4
- -5
- -6
- -7
(-4,-9)
S
- -8
- -9
--10
- -11
2
3
4
5
6
7
8
9
2. suppose you are given a coordinate system determine the quadrant in which the
following points lie:
1 A (4,5)
2 B (-4,-5)
3C (4,-5)
ANS: A (4,5)
lies in the first quadrant
B (-4,-5)
lies in the third quadrant
C (4,-5)
lies in the fourth quadrant
3. suppose P is a point with coordinates (-8,3) with respect to a coordinate system
XꜗOX ↔ YꜗOY. Let XꜗOX ↔ Yꜗ1O1Y1 be another system with XꜗOX Xꜗ1O1X1
and suppose O1 has coordinates (9,5) with respect to XꜗOX ↔ YꜗOY what are the
coordinates of P in the system Xꜗ1O1X1 ↔ Yꜗ1O1Y1 ?
P(-8,3)
XꜗOX ↔ YꜗOY
O(9,5)
XꜗOX ↔ YꜗOY
ANS : (-17,-2)
(-8-9,-3-5)
(-17,-2)
4. Suppose P has coordinates (10,2) in a coordinate system X’OX ↔ Y’OY and (-3,-6)
in another coordinate system X’1O1X1 ↔ Y’1O1Y1 with X’OX ↔ X’1O1X1
determine the coordinates of O with respect to the system X’1O1X1 ↔ Y’1O1Y1.
P(10,2) X’OX ↔ Y’OY
(-3,-6) X’1O1X1 ↔ Y’1O1Y1
ANS: (-13,-8)
(-13,-8)
(-3-10,-6-2)
EXERCISE 2.5.4
1. Draw the graphs of the following straight lines:
(i)4y=-x+3
X=1
x
y
1
0.5
5
-1
-0.5 1
X=-1
4y=-1+3
4Y=(-1)+3
Y= 2 = 1 =0.5
4 2
X = +5
4Y = -5+3
4Y = -2
=1+3=4
Y = 4 =1
4
Y = -2 = -0.5
4
4y=x+3
(1,-5)
-9 -8 -7 -6 -5 -4 -3 -2 -1
1
2
3
4
5
6
7
(ii) 3y = 4x + 1
X
Y
2
3
5
7
8
11
-1
-1
X=2
3y = 4x + 1
3y = 4 * 2 + 1 =8 + 1 =9
Y=9=3
3
3y = 4x – 1 + 1
= -4+1 = -3
Y = -3 = -1
3
X=5
3y = 4 * 5 +1 = 21
Y = 21 = 7
3
X=8
3y =32 + 1 =33
--8
Y =11
--7
(5,7)
--6
--5
- -4
--3
--2
--1
-9 -8 -7 -6 -5 -4 -3 -2 -1
(-1,-1)
(3y=4x+1)
-
(2,3)
(iii) x = 4
(iv) 3y = 1
3y = 0x + 1
X
y
Y
0
1
3
0.3
1
1
3
0.3
2
1
3
0.3
3
1
3
0.3
4
1
3
0.3
-
5
3y = 1
4
X
X
X
3
X
X
X
X
2
1
-5
-4 -3
-2
-1
0
1
-1
-2
-3
-4
2
3
4
5
2. Draw the graph of y = y + 1
X x +2
Y(x+2) = x(y+1)
Xy + 2y = xy + x
2y = x
X
0
1
2
3
4
Y
0
2
4
6
8
--8
--7
--6
--5
- -4
--3
--2
--1
-9 -8 -7 -6 -5 -4 -3 -2 -1
2y = x
1
- -1
- -2
- -3
- -4
- -5
- -6
- -7
2
3
4
5
6
7
3. Determine the equation of the line in each of the following graphs:
y
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
x
-5
-4
-3
-2
-1
2y = x
0
1
- -1
- -2
- -3
2
3 4
5
6
7
8
9 10 11 12
y
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
x
-5
-4
-3
-2
-1
2y = x
0
1
2
3 4
5
6
7
8
9 10 11 12
- -1
- -2
- -3
(1) X = 2
Y=0
x =0
x=3
y = -3
y=4
Ans: 3x – 2y = 6
(2) X = 0
Y= 5
X + y =5
x=5
y=0
4. A boat is moving in a river ,down stream .whose stream has speed 8km per
hour. The speed of the motor of the boat is 22 km per hour. Draw the graph of
the distance covered by the boat versus hour.
Speed of the stream = 8km per hour
Speed of the motor boat = 22km per hour
Speed of the motor boat down stream = 30 km per hour
Number of hours x
Distance covered Y kms
1 2 3
30 60 90
4
120
-150
-120
-90
-60
-30
1
2
3
4
5
6
No of hours
-
-
5. Find the point of intersection of the straight lines 3y+4x =7 and 4y+3x= 7
By drawing their graphs and looking for the point where they meet.
3y + 4x =7 and
x
Y
1
1
4
-3
4y + 3x = 7
-1
5
X
Y
1
1
3
-0.5
2
0.25
3y + 4x =7
3y + 4*1 =7
3y + 4 = 7
3y = 7 – 4 = 3
Y=1
3y + 3x =7
3y – 8 = 7
3y = 7 + 8
y=5
3y + 16 = 7
3y = 7 -16 = -9
4y + 3*3 = 7
4y = 7 -3 =4
Y=1
4y + 3*3 =7
4y = 7-9 = -2
Y = -2 = -1
4
2
4y + 3*2 = 7
4y + 6 =7
4y =7 – 6
Y = 1 = 0.25
4
y
-10
-9
-8
3y+4x=7
-7
-6
-5
4y+3y=7
-4
-3
-2
-1
x
-6
-5
-4
-3
-2
-1
0
1
2
- -1
- -2
- -3
- -4
- -5
- -6
Inter sects point is (1,1)
3 4
5
6
7
1. Choose a correct option :
(a) A The point (4,0) lie on the line………
a) y-x=0
b) y=0
c) x=0
d) y+x=0
(b) The point (-5,4) lie in…
a) the first quadrant
b)the second quadrant
c)the third quadrant
d)the fourth quadrant
c. If a straight – line pass through (0 ,0) and (1,5) then its equation is…
a) y=x
b) y=5x
c) 5y=x
d) y=x+5
d. If a point p has coordinate (3,4) in a coordinate system X’OX ↔Y’OY and if o
has coordinates (4,3) in another system X’1O1X1↔ Y’1O1Y1
C) (7, 7)
D) (-1, 1)
e . The coordinate of a point p in a system X’OX ↔Y’OY are (5, 8). The coordinate
of same point in the system Y’OY ↔X’OX are……
a) (-8 ,5)
b) (8,5)
c) (8 ,-5)
d)(-8, -5)
f. The signs of the coordinates of a point in the third quadrant are……
a) (+, -)
b) (-, +)
c) (+ , +)
d) (-, -)
g . If person moves either 1 unit in the direction of positive x-axis or 1 unit in the
direction of positive y- axis per step, then the number of steps he requires to
reach the number (10,12)
starting from the origin (0,0) is…….
a) 10
b)12
c)22
d)120
h. The y-coordinate of the point of intersection of the line y=3x+4 with x=3 is……
a) 4
b)7
c)10 d)13
i. The equation of the line which passes through (0,0) and (1,1) is….
a) y=x
b) y=-x
c) y=1
d) x=1
2.Find the quadrant in which the following points lie :
a.
b.
c.
d.
(5, 10) = 1s t quadrant
(-8, 9) = 2nd quadrant
(-800, -300) = 3rdt quadrant
(8 -100) = 4th quadrant
3.Match the following :
A) on the x –axis
1) x coordinate is negative
B) in the second quadrant
2) cuts the y – axis at (0 ,4)
c) the line y=3x+4
3) coordinates of a point are of
the form (a ,0)
Ans : A-iii
B- I
C- ii
4. Fill in the blanks :
a) The y – coordinate of a point on the x – axis is ….. (zero)
b) The x – coordinate is called as……(abscissa)
c) The x –axis and y –axis intersect at ….(0,0)
d) If a point ( x ,y) ≠ (0 , 0) is in the third q u a d r a n t (-ve)
e) If a point (x ,y ) lies above horizontal axis then y is is always ….(+ve)
f) The point of intersection of x=y and x= -y is ….. (0 , 0)
g) The line y=4x+5 intersects y-axis at the point….(0,5)
5.True or false?
a) The equation of the X-axis is X=0. (false)
b) The line X=4 is parallel to y – axis.(true)
c) The line y=8 is perpendicular to x-axis. (False)
d) The lines x=y & x=-y are perpendicular to each other. (True)
e) The lines x=9 and y=9 are perpendicular to each other. (True)
f) The graph of y = x2 is a straight line.(False)
g) The graph y=3x+4 does not intersect x-axis. (False)
h) In a rectangular coordinate system, the coordinate axes are choosen such that
they form a pair of perpendicular lines. (True)
6. Determines the equation of the line which passes through the point (0,-8) and
(7,0).
7y = 8(x-7)
7y = 8x – 56
8. A point P has coordinates (7,10) in a coordinate system X’OX ↔ Y’OY. Suppose
it has coodinates (10,7)in another coordinate system X’1O1X1 ↔ Y’1O1Y1 with
X’OX || X’1O1X1. Find the coordinates of 0 1 in the system X’OX ↔ Y’OY.
Ans : (-3,3)
9. Sketch the region {(x,y): xx >= 0, y>= 0, x+2y <= 4 } in a coordinate system set up
by you.
Ans: Let x+2y <= 4
Let x = 0 0 + 2y = 4
Y =2
1 + 2y = 4
2y = 3
2 + 2y = 4
2y = 2
Y= 1
Y =3
2
3 + 2y = 4
2y = 4-3 = 1
y=1
2
x=0 y=2
x =1 y=3
2
x =2 y=1
x =3 y=1
2
x = -1 y = 5
2
4 + 2y <= 4
-1 + 2y <= 4
2y<= 0
2y = 4+1 = 5
y<=0
y=5
2
-7
-6
-5
-4
-3
-2
-1
x
-6
-5
-4
-3
-2
-1
0
1
2
3 4
5
6
7
8
9
- -1
- -2
- -3
- -4
- -5
- -6
10. Draw the graph of lines 3y = 4x – 4 and 2x = 3y + 4 and determine the point at
which these lines meet.
1. 3y = 4x-4
X
1
4
7
10
Y
0
4
8
12
3y = 4*1-4
3y = 4-4 = 0
Y=0
3y = 4*4-4
3y = 16-4 = 12
y=4
3y = 4*7-4
3y = 28-4
3y = 24
3y = 4*10-4
3y = 40-4
3y = 36
Y = 24 = 8
3
y = 12
1. 2x = 3y + 4
X
5
Y
2
8
4
11
6
-1
-2
2*5 = 3y+4
10-4 = 3y
3y = 6
Y=6=2
3
2*11 = 3y+4
22-4 = 3y
3y = 18
Y= 6 = 2
3
2*8 = 3y+4
16-4=3y
12 = 3y
y =12 =4
3
2*-1=3y+4
-2-4 =3y
-6 = 3y
y = -6 =-2
3
-7
-6
-5
-4
-3
-2
-1
x
-6
-5
-4
-3
-2
-1
0
1
2
3 4
5
6
7
- -1
2x=3y+1
- -2
- -3
3y=4x-4
- -4
- -5
Intersets point (0,-1.33)
8
9
11. If a*b = ab + a + b, draw the graph of Y = 3 * x + 1 * 2.
a * b= ab + a + b
y = 3 * x1 + 1 * 2
x= 0
y= 3 *0 + 1* 2
= 3*0+3+0+1*2+1+2
=0 + 3 + 2 + 3
=0
X=1
Y = 3 *1 + 1*2
= 3*1+3+1+1*2+1+2
= 3+4+2+3
=12
X = -1
Y = 3*(-1)+1*2
=3*(-1)+3+(-1)+1*2+1+2
=-3+2+2+3
=4
X
Y
0
8
-1
4
1
12
-
-12
(1,12)
-11
-10
-9
-8 (1,8)
-7
-6
-5
(-1,4)
-4
-3
-2
-1
x
-6
-5
-4
-3
-2
-1
0
1
2
3 4
5
6
7
8
9