EduSahara™ Assignment
Name : Parallel and Perpendicular Lines
Chapter : Equation of a Straight Line
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
The slope of x-axis is
(i)
90
(ii)
0
(iii)
-1
(iv)
1
(v)
undefined
Question
2
2.
The slope of y-axis is
(i)
-1
(ii)
90
(iii)
undefined
(iv)
1
(v)
0
Question
3
3.
The slope of the line joining the points
(
(
−
6
)
,
(
−
6
)
)
and
(
(
−
7
)
,
5
)
is
(i)
-9
(ii)
-12
(iii)
-11
(iv)
-13
(v)
-10
Question
4
4.
The slope of the line perpendicular to the line passing through
the points
(
(
−
1
)
,
5
)
and
(
1
,
4
)
is
(i)
3
(ii)
4
(iii)
2
(iv)
1
(v)
0
Question
5
5.
Two straight lines are parallel if and only if their slopes are
(i)
undefined
(ii)
1
(iii)
0
(iv)
equal
(v)
unequal
Question
6
6.
Two straight lines are perpendicular if and only if the product of their slopes is
(i)
1
(ii)
-1
(iii)
0
(iv)
undefined
(v)
90
Question
7
7.
The slope of a line parallel to the line
(
−
8
x
−
7
y
−
5
)
=
0
is
(i)
(
-10
9
)
(ii)
(
-8
7
)
(iii)
(
-6
7
)
(iv)
(
-6
5
)
(v)
(
-10
7
)
Question
8
8.
The slope of a line perpendicular to the line
(
3
x
−
6
y
−
27
)
=
0
is
(i)
-1
(ii)
-2
(iii)
-5
(iv)
-3
(v)
0
Question
9
9.
The equation of x-axis is
(i)
x
=
0
(ii)
y
=
x
(iii)
x
=
1
(iv)
y
=
1
(v)
y
=
0
Question
10
10.
The equation of y-axis is
(i)
y
=
0
(ii)
x
=
1
(iii)
y
=
x
(iv)
x
=
0
(v)
y
=
1
Question
11
11.
The equation of the line passing through
(
(
−
6
)
,
3
)
and parallel to the line
(
−
6
x
+
3
y
+
12
)
=
0
is
(i)
(
−
6
x
+
3
y
+
15
)
=
0
(ii)
(
−
6
x
+
3
y
−
45
)
=
0
(iii)
(
7
x
−
4
y
−
14
)
=
0
(iv)
(
3
x
+
8
y
−
6
)
=
0
(v)
(
x
−
y
+
1
)
=
0
Question
12
12.
The equation of the line passing through
(
1
,
1
)
and perpendicular to the line
(
−
2
y
+
6
)
=
0
is
(i)
(
4
x
+
13
y
−
71
)
=
0
(ii)
(
x
−
1
)
=
0
(iii)
(
−
2
x
+
7
y
−
5
)
=
0
(iv)
(
x
+
5
)
=
0
(v)
(
4
x
+
11
y
−
57
)
=
0
Question
13
13.
The equation of the line passing through
(
1
,
7
)
and parallel to the join of points
(
3
,
6
)
and
(
8
,
(
−
5
)
)
is
(i)
(
12
x
+
7
y
−
61
)
=
0
(ii)
(
x
+
2
y
−
15
)
=
0
(iii)
(
2
x
+
y
−
12
)
=
0
(iv)
(
x
−
y
+
6
)
=
0
(v)
(
11
x
+
5
y
−
46
)
=
0
Question
14
14.
The equation of the line passing through
(
8
,
1
)
and perpendicular to the join of points
(
1
,
8
)
and
(
(
−
5
)
,
(
−
4
)
)
is
(i)
(
−
7
x
−
7
y
+
63
)
=
0
(ii)
(
5
x
−
13
y
−
27
)
=
0
(iii)
(
x
+
2
y
−
10
)
=
0
(iv)
(
−
5
x
+
8
y
+
32
)
=
0
(v)
(
−
12
x
+
y
+
4
)
=
0
Question
15
15.
The slope of any line parallel to x-axis is
(i)
1
(ii)
-1
(iii)
90
(iv)
zero
(v)
undefined
Question
16
16.
The slope of any line parallel to y-axis is
(i)
90
(ii)
zero
(iii)
-1
(iv)
1
(v)
undefined
Question
17
17.
The ratio of coefficients of x and y in the equations of any two parallel lines is
(i)
not proportional
(ii)
not same
(iii)
2
(iv)
same
(v)
1
Question
18
18.
Two non-vertical lines are parallel if and only if their slopes are
(i)
not proportional
(ii)
same
(iii)
not same
(iv)
1
(v)
2
Question
19
19.
Any line parallel to x-axis is
(i)
an oblique line
(ii)
a curved line
(iii)
a horizontal line
(iv)
a vertical line
Question
20
20.
Any line parallel to y-axis is
(i)
an oblique line
(ii)
a curved line
(iii)
a vertical line
(iv)
a horizontal line
Question
21
21.
A line which is neither parallel to x-axis nor y-axis is
(i)
a curved line
(ii)
an oblique line
(iii)
a vertical line
(iv)
a horizontal line
Question
22
22.
Which of the following are true?
a)
Slope of any line parallel to x-axis is not defined
b)
Slope of any line parallel to y-axis is not defined
c)
Slope of any line parallel to x-axis is zero
d)
Slope of any line parallel to y-axis is zero
(i)
{b,c}
(ii)
{a,b}
(iii)
{d,c}
(iv)
{a,d,b}
(v)
{a,c,b}
Question
23
23.
Which of the following are true ?
a)
Equations of two parallel lines have the same constant and coefficients of x and y will not be same
b)
Equations of two parallel lines have the same constant and coefficients of x and y will be same
c)
Equations of two parallel lines differ in the constant and coefficients of x and y will not be same
d)
Equations of two parallel lines differ in the constant term only, coefficients of x and y will be same
(i)
{a,d}
(ii)
{d}
(iii)
{b,d}
(iv)
{c,a,d}
Question
24
24.
Equation of a straight line which is parallel to x-axis (where k is a constant) is
(i)
x
=
y
(ii)
x
=
0
(iii)
y
=
0
(iv)
y
=
k
(v)
x
=
k
Question
25
25.
Equation of a straight line which is parallel to y-axis (where k is a constant) is
(i)
x
=
y
(ii)
y
=
k
(iii)
x
=
k
(iv)
x
=
0
(v)
y
=
0
Question
26
26.
The slope of the line
a
x
+
b
y
+
c
= 0
is
(i)
-b
a
(ii)
c
(iii)
-a
b
(iv)
b
(v)
a
Question
27
27.
In equation of the line
y
=
m
x
+
c
, the slope is
(i)
y
(ii)
x
(iii)
m
(iv)
c
(v)
undefined
Question
28
28.
Find the equation parallel to the given equation
(i)
(
x
+
6
y
+
5
)
=
0
(ii)
(
−
5
x
+
6
y
+
57
)
=
0
(iii)
(
−
6
x
+
y
+
3
)
=
0
(iv)
(
7
x
+
6
y
+
14
)
=
0
Question
29
29.
Find the equation perpendicular to the given equation
(i)
(
−
3
x
−
5
y
−
3
)
=
0
(ii)
(
−
5
x
+
3
y
−
6
)
=
0
(iii)
(
−
5
x
−
3
y
+
7
)
=
0
(iv)
(
3
x
+
5
y
+
34
)
=
0
Question
30
30.
Find the equation parallel to the given equation
(
−
8
x
+
2
y
+
3
)
=
0
(i)
(
−
8
x
+
2
y
+
2
)
=
0
(ii)
(
−
3
x
+
4
y
−
8
)
=
0
(iii)
(
−
10
x
+
2
y
−
30
)
=
0
(iv)
(
x
+
4
y
+
6
)
=
0
Question
31
31.
Find the equation perpendicular to the given equation
(
3
x
+
2
y
+
5
)
=
0
(i)
(
−
2
x
+
3
y
+
4
)
=
0
(ii)
(
x
+
2
y
−
13
)
=
0
(iii)
(
3
x
+
2
y
−
1
)
=
0
(iv)
(
−
5
x
+
3
y
−
42
)
=
0
Question
32
32.
Find the slope of the displayed line
(i)
2
(ii)
2
3
(iii)
0
(iv)
2
5
(v)
4
3
Question
33
33.
The equation of the x-axis is
a)
x
=
y
b)
x
=
1
c)
y
=
0
d)
y
=
1
e)
x
=
0
(i)
{a,c}
(ii)
{c}
(iii)
{b,c}
(iv)
{d,e,c}
Question
34
34.
Find the equation of a straight line parallel to x-axis and
passing through the point
(
(
−
9
)
,
3
)
(i)
y
=
5
(ii)
y
=
2
(iii)
x
=
(
−
6
)
(iv)
y
=
3
(v)
x
=
(
−
9
)
Question
35
35.
Find the equation of a straight line parallel to y-axis and
passing through the point
(
(
−
6
)
,
4
)
(i)
y
=
4
(ii)
y
=
7
(iii)
x
=
(
−
7
)
(iv)
x
=
(
−
6
)
(v)
x
=
(
−
4
)
Question
36
36.
The equation of the line passing through
(
x
1
,
y
1
)
and parallel to the line
a
x
+
b
y
+
c
= 0
is
(i)
(
y
−
y
1
) =
-a
b
(
x
−
x
1
)
(ii)
(
y
−
y
1
) =
b
a
(
x
−
x
1
)
(iii)
(
y
−
y
1
) =
a
b
(
x
−
x
1
)
(iv)
(
y
−
y
1
) =
c
b
(
x
−
x
1
)
Question
37
37.
The equation of the line passing through
(
x
1
,
y
1
)
and perpendicular to the line
a
x
+
b
y
+
c
= 0
is
(i)
(
y
−
y
1
) =
b
a
(
x
−
x
1
)
(ii)
(
y
−
y
1
) =
-a
b
(
x
−
x
1
)
(iii)
(
y
−
y
1
) =
c
b
(
x
−
x
1
)
(iv)
(
y
−
y
1
) =
a
b
(
x
−
x
1
)
Question
38
38.
The slope of the line passing through the points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
(i)
x
2
+
y
1
y
2
+
x
1
(ii)
x
2
+
x
1
y
2
+
y
1
(iii)
x
2
−
y
1
y
2
−
x
1
(iv)
y
2
−
y
1
x
2
−
x
1
(v)
x
2
−
x
1
y
2
−
y
1
Question
39
39.
The equation of the line parallel to
(
3
x
+
12
y
−
48
)
=
0
and making a y-intercept of
4
is
(i)
(
x
+
4
y
−
16
)
=
0
(ii)
(
−
2
x
−
8
y
+
32
)
=
0
Question
40
40.
The equation of the line perpendicular to
(
−
x
−
9
y
−
28
)
=
0
and making a y-intercept of
(-8)
is
(i)
(
−
4
x
+
8
y
+
64
)
=
0
(ii)
(
2
x
+
11
y
+
28
)
=
0
(iii)
(
x
+
2
y
+
7
)
=
0
(iv)
(
−
9
x
+
y
+
8
)
=
0
(v)
(
−
5
x
−
y
−
8
)
=
0
Question
41
41.
Find the value of k such that
(
3
x
−
7
y
−
32
)
=
0
and
(
k
x
+
7
y
+
15
) = 0
are parallel to each other
(i)
-3
(ii)
-1
(iii)
-2
(iv)
-4
(v)
-6
Question
42
42.
Find the value of k such that
(
9
x
+
2
y
+
68
)
=
0
and
(
k
x
+
9
y
+
12
) = 0
are perpendicular to each other
(i)
-5
(ii)
-2
(iii)
-3
(iv)
-1
(v)
0
Question
43
43.
Find equation of the right bisector of the line segment
joining the points
(
(
−
5
)
,
2
)
and
(
4
,
3
)
(i)
(
−
x
+
9
y
−
56
)
=
0
(ii)
(
9
x
+
y
+
43
)
=
0
(iii)
(
18
x
+
2
y
+
4
)
=
0
(iv)
(
9
x
+
y
+
12
)
=
0
(v)
(
9
x
+
y
−
39
)
=
0
Question
44
44.
(
(
−
7
)
,
(
−
1
)
)
,
(
(
−
8
)
,
7
)
and
(
4
,
(
−
3
)
)
are the vertices of triangle ABC.
Find the equation of the altitude of the triangle through vertex C
(i)
(
−
x
+
5
y
+
28
)
=
0
(ii)
(
−
11
x
+
2
y
−
102
)
=
0
(iii)
(
−
6
x
+
5
y
−
37
)
=
0
(iv)
(
−
x
+
10
y
+
28
)
=
0
(v)
(
−
x
+
8
y
+
28
)
=
0
Question
45
45.
(
7
,
3
)
,
(
(
−
6
)
,
4
)
and
(
8
,
5
)
are the vertices of triangle ABC.
Find the equation of the median of the triangle through vertex C
(i)
(
3
2
x
−
13
2
y
+
51
2
)
=
0
(ii)
(
3
2
x
−
15
2
y
+
51
2
)
=
0
(iii)
(
−
3
2
x
−
6
y
+
57
2
)
=
0
(iv)
(
3
2
x
−
17
2
y
+
51
2
)
=
0
(v)
(
27
2
y
−
54
)
=
0
Question
46
46.
Find the equation of the line which is parallel to the line
(
−
x
−
2
y
+
9
)
=
0
and
making a y-intercept of
(-7)
(i)
(
−
2
x
−
2
y
+
7
)
=
0
(ii)
(
2
y
+
14
)
=
0
(iii)
(
x
+
4
y
+
14
)
=
0
(iv)
(
x
+
2
y
+
14
)
=
0
(v)
(
−
2
x
+
y
+
7
)
=
0
Question
47
47.
Find the x-intercept of the line which is parallel to the line
(
2
x
+
12
y
+
48
)
=
0
and
making a y-intercept of
(-3)
(i)
-17
(ii)
-20
(iii)
-19
(iv)
-18
(v)
-16
Question
48
48.
The points B
(
(
−
3
)
,
10
)
and D
(
(
−
11
)
,
8
)
are the opposite vertices
of a square ABCD. Find the equation of the diagonal AC
(i)
(
−
2
x
+
5
y
−
86
)
=
0
(ii)
(
7
x
+
2
y
+
38
)
=
0
(iii)
(
8
x
+
2
y
+
38
)
=
0
(iv)
(
8
x
+
5
y
+
38
)
=
0
(v)
(
−
2
x
+
8
y
−
86
)
=
0
Question
49
49.
Which of the following pairs of lines are parallel?
(i)
(
−
10
x
+
10
y
−
10
)
=
0
,
(
x
+
y
−
1
)
=
0
(ii)
(
−
10
x
+
10
y
−
10
)
=
0
,
(
−
10
x
+
10
y
+
70
)
=
0
(iii)
(
−
10
x
+
10
y
−
10
)
=
0
,
(
−
20
x
+
10
y
+
110
)
=
0
(iv)
(
−
10
x
+
10
y
−
10
)
=
0
,
(
y
+
2
)
=
0
Question
50
50.
Which of the following pairs of lines are perpendicular?
(i)
(
7
x
+
14
y
−
35
)
=
0
,
(
−
2
x
+
y
+
12
)
=
0
(ii)
(
7
x
+
14
y
−
35
)
=
0
,
(
−
3
x
+
y
+
20
)
=
0
(iii)
(
7
x
+
14
y
−
35
)
=
0
,
(
x
+
2
y
−
7
)
=
0
(iv)
(
7
x
+
14
y
−
35
)
=
0
,
(
−
x
+
2
y
+
7
)
=
0
Question
51
51.
The slope of a line is the tangent of the angle made by the line with the
(i)
positive y-axis
(ii)
positive x-axis
(iii)
negative x-axis
(iv)
negative y-axis
Question
52
52.
Find the relation between x and y if the points
(
x
,
y
)
,
(
5
,
(
−
4
)
)
and
(
8
,
(
−
3
)
)
are collinear
(i)
(
2
x
+
2
y
−
2
)
=
0
(ii)
(
x
+
5
y
+
7
)
=
0
(iii)
(
2
x
+
6
y
+
2
)
=
0
(iv)
(
x
−
3
y
−
17
)
=
0
(v)
(
x
+
y
−
1
)
=
0
Question
53
53.
Find the coordinates of the orthocentre of the triangle
whose vertices are
(
(
−
6
)
,
(
−
6
)
)
,
(
7
,
5
)
and
(
(
−
6
)
,
3
)
(i)
(
(
−
87
13
)
,
4
)
(ii)
(
(
−
126
13
)
,
3
)
(iii)
(
(
−
100
13
)
,
5
)
(iv)
(
(
−
74
13
)
,
7
)
(v)
(
(
−
113
13
)
,
6
)
Question
54
54.
The point of intersection of x-axis and y-axis
(i)
(
0
,
0
)
(ii)
(
1
,
1
)
(iii)
(
1
,
0
)
(iv)
(
0
,
5
)
Question
55
55.
Find the value of k such that the points
(
(
−
8
)
,
1
)
,
(
(
−
19
3
)
,
10
3
)
and
(k,8)
are collinear
(i)
-4
(ii)
-2
(iii)
-3
(iv)
-6
(v)
0
Question
56
56.
Find the value of k such that the points
(
(
−
4
)
,
2
)
,
(
(
−
27
7
)
,
3
)
and
(-3,k)
are collinear
(i)
8
(ii)
10
(iii)
6
(iv)
9
(v)
12
Question
57
57.
Which of the following sets of points are collinear?
(i)
(
(
−
8
)
,
6
)
,
(
3
,
(
−
7
)
)
,
(
(
−
81
17
)
,
37
17
)
(ii)
(
0
,
2
)
,
(
(
−
3
)
,
7
)
,
(
0
,
5
)
(iii)
(
(
−
8
)
,
(
−
1
)
)
,
(
(
−
4
)
,
(
−
3
)
)
,
(
(
−
8
)
,
(
−
7
)
)
(iv)
(
4
,
(
−
7
)
)
,
(
0
,
5
)
,
(
0
,
1
)
(v)
(
4
,
1
)
,
(
8
,
(
−
2
)
)
,
(
(
−
4
)
,
(
−
8
)
)
Question
58
58.
The points B
(
(
−
3
)
,
5
)
and D
(
(
−
10
)
,
4
)
are the opposite vertices
of a square ABCD. Find the other two vertices
(i)
(
(
−
4
)
,
3
)
,
(
(
−
7
)
,
8
)
(ii)
(
(
−
6
)
,
1
)
,
(
(
−
7
)
,
8
)
(iii)
(
(
−
8
)
,
(
−
1
)
)
,
(
(
−
7
)
,
8
)
(iv)
(
(
−
5
)
,
0
)
,
(
(
−
7
)
,
8
)
(v)
(
(
−
6
)
,
1
)
,
(
(
−
8
)
,
9
)
Question
59
59.
Find the coordinates of the circumcentre of the triangle
whose vertices are
(
4
,
(
−
2
)
)
,
(
1
,
(
−
4
)
)
and
(
(
−
1
)
,
6
)
(i)
(
63
34
,
101
34
)
(ii)
(
29
34
,
(
−
1
34
)
)
(iii)
(
(
−
73
34
)
,
(
−
35
34
)
)
(iv)
(
(
−
39
34
)
,
67
34
)
(v)
(
(
−
5
34
)
,
33
34
)
Assignment Key
1) (ii)
2) (iii)
3) (iii)
4) (iii)
5) (iv)
6) (ii)
7) (ii)
8) (ii)
9) (v)
10) (iv)
11) (ii)
12) (ii)
13) (v)
14) (iii)
15) (iv)
16) (v)
17) (iv)
18) (ii)
19) (iii)
20) (iii)
21) (ii)
22) (i)
23) (ii)
24) (iv)
25) (iii)
26) (iii)
27) (iii)
28) (i)
29) (ii)
30) (i)
31) (i)
32) (ii)
33) (ii)
34) (iv)
35) (iv)
36) (i)
37) (i)
38) (iv)
39) (i)
40) (iv)
41) (i)
42) (ii)
43) (iii)
44) (v)
45) (ii)
46) (iv)
47) (iv)
48) (iii)
49) (ii)
50) (i)
51) (ii)
52) (iv)
53) (iii)
54) (i)
55) (iii)
56) (iv)
57) (i)
58) (ii)
59) (v)
