EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Coordinate Geometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Which of the following is a point on the positive y-axis?
(i)
(
0
,
(
−
9
)
)
(ii)
(
0
,
9
)
(iii)
(
(
−
5
)
,
9
)
(iv)
(
6
,
0
)
(v)
(
(
−
3
)
,
0
)
Question
2
2.
Which of the points (7,6), (-5,5), (-6,-6) and (6,-7) belong to the third quadrant?
(i)
(
(
−
6
)
,
(
−
6
)
)
(ii)
(
7
,
6
)
(iii)
(
6
,
(
−
7
)
)
(iv)
(
(
−
5
)
,
5
)
Question
3
3.
The centroid of the triangle formed by the points
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
and
(
x
3
,
y
3
)
is
(i)
(
x
1
−
x
2
−
x
3
2
,
y
1
−
y
2
−
y
3
2
)
(ii)
(
x
1
−
x
2
−
x
3
3
,
y
1
−
y
2
−
y
3
3
)
(iii)
(
y
1
−
y
2
−
y
3
2
,
x
1
−
x
2
−
x
3
2
)
(iv)
(
y
1
+
y
2
+
y
3
2
,
x
1
+
x
2
+
x
3
2
)
(v)
(
x
1
+
x
2
+
x
3
3
,
y
1
+
y
2
+
y
3
3
)
Question
4
4.
Find the coordinates of the mid points of the sides of the triangle formed by
(
0
,
(
−
3
)
)
,
(
(
−
3
)
,
(
−
3
)
)
and
(
(
−
1
)
,
3
)
(i)
(
(
−
3
2
)
,
(
−
3
)
)
,
(
(
−
2
)
,
0
)
,
(
(
−
5
2
)
,
(
−
2
)
)
(ii)
(
(
−
5
2
)
,
(
−
2
)
)
,
(
(
−
2
)
,
0
)
,
(
(
−
1
2
)
,
0
)
(iii)
(
(
−
3
2
)
,
(
−
3
)
)
,
(
(
−
2
)
,
0
)
,
(
(
−
1
2
)
,
0
)
(iv)
(
(
−
3
2
)
,
(
−
3
)
)
,
(
(
−
2
)
,
0
)
,
(
1
2
,
(
−
1
)
)
(v)
(
(
−
3
2
)
,
(
−
3
)
)
,
(
0
,
2
)
,
(
(
−
1
2
)
,
0
)
Question
5
5.
Find the coordinates of the midpoints of the sides of the quadrilateral
formed by
(
(
−
5
)
,
(
−
1
)
)
,
(
(
−
1
)
,
2
)
,
(
(
−
5
)
,
4
)
and
(
(
−
6
)
,
3
)
(i)
(
(
−
3
)
,
1
2
)
,
(
(
−
3
)
,
3
)
,
(
(
−
9
2
)
,
5
2
)
,
(
(
−
11
2
)
,
1
)
(ii)
(
(
−
3
)
,
1
2
)
,
(
(
−
3
)
,
3
)
,
(
(
−
11
2
)
,
7
2
)
,
(
(
−
13
2
)
,
2
)
(iii)
(
(
−
3
)
,
1
2
)
,
(
(
−
3
)
,
3
)
,
(
(
−
11
2
)
,
7
2
)
,
(
(
−
11
2
)
,
1
)
(iv)
(
(
−
1
)
,
5
2
)
,
(
(
−
3
)
,
3
)
,
(
(
−
11
2
)
,
7
2
)
,
(
(
−
11
2
)
,
1
)
(v)
(
(
−
3
)
,
1
2
)
,
(
(
−
3
)
,
3
)
,
(
(
−
15
2
)
,
3
2
)
,
(
(
−
11
2
)
,
1
)
Question
6
6.
The point
(
9
,
(
−
1
)
)
lies in
(i)
fourth quadrant
(ii)
first quadrant
(iii)
third quadrant
(iv)
second quadrant
Question
7
7.
Some volunteers on a cleanliness drive decided to clean an open ground in the shape of a quadrilateral ABCD, where AB = 17.00 m, BC = 16.00 m, CD = 12.00 m, and DA = 20.00 m. They split into two groups m and n and started cleaning on either sides of the diagonal BD. Group m marked their perimeter which is of length 55 m. Which group cleaned more area ? Find the total area cleaned by both groups.
(i)
group m
,
239.60 sq.m
(ii)
group n
,
255.60 sq.m
(iii)
group m
,
230.60 sq.m
(iv)
group m
,
237.60 sq.m
(v)
group m
,
221.60 sq.m
Question
8
8.
Which of the following lines pass through the origin?
(i)
(
−
10
x
+
4
y
−
18
)
=
0
(ii)
(
4
x
−
13
y
−
84
)
=
0
(iii)
(
−
2
x
+
7
y
−
16
)
=
0
(iv)
(
4
x
−
6
y
)
=
0
(v)
(
8
x
+
2
y
−
56
)
=
0
Question
9
9.
The point
(
1
,
9
)
lies in
(i)
first quadrant
(ii)
third quadrant
(iii)
second quadrant
(iv)
fourth quadrant
Question
10
10.
Which of the following are true?
a)
The ordinate of every point on x-axis is zero
b)
The abscissa of every point on x-axis is zero
c)
The ordinate of every point on y-axis is zero
d)
The abscissa of every point on y-axis is zero
(i)
{b,d,a}
(ii)
{b,c,a}
(iii)
{c,d}
(iv)
{a,d}
(v)
{b,a}
Question
11
11.
A triangular park has sides 100 m, 170 m and 140 m. A gardener has to put a fence all around it and also plant grass inside. Find the cost of fencing it with barbed wire at the rate of ₹11 per metre leaving a space of 4 m wide for the gate on one side.
(i)
₹4306.00
(ii)
₹4466.00
(iii)
₹4716.00
(iv)
₹4586.00
Question
12
12.
In a coordinate geometry plane, the vertical reference line is called
(i)
ordinate
(ii)
abscissa
(iii)
origin
(iv)
y-axis
(v)
x-axis
Question
13
13.
A triangular park has sides 150 m, 150 m and 100 m. A gardener has to put a fence all around it and also plant grass inside. How much area does he need to plant ?
(i)
7251.07 sq.m
(ii)
7311.07 sq.m
(iii)
7021.07 sq.m
(iv)
6931.07 sq.m
(v)
7071.07 sq.m
Question
14
14.
Find the perimeter of the triangle formed by the points
(
(
−
8
)
,
(
−
2
)
)
,
(
0
,
6
)
and
(
3
,
(
−
1
)
)
(i)
(
8
√
2
+
√
58
+
4
√
122
)
(ii)
(
8
√
2
+
√
58
+
√
122
)
(iii)
(
8
√
2
+
√
61
+
√
122
)
(iv)
(
8
√
2
+
√
58
+
122
)
(v)
(
8
√
2
+
√
56
+
√
122
)
Question
15
15.
The slope of the line passing through the points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
(i)
x
2
+
x
1
y
2
+
y
1
(ii)
y
2
−
y
1
x
2
−
x
1
(iii)
x
2
−
y
1
y
2
−
x
1
(iv)
x
2
+
y
1
y
2
+
x
1
(v)
x
2
−
x
1
y
2
−
y
1
Question
16
16.
Find the lengths of the sides of the triangle formed by the points
(
1
,
0
)
,
(
3
,
(
−
5
)
)
and
(
(
−
6
)
,
1
)
(i)
√
29
,
3
√
13
,
5
√
4
(ii)
√
29
,
39
,
5
√
2
(iii)
4
√
29
,
3
√
13
,
5
√
2
(iv)
√
29
,
3
√
13
,
5
√
2
Question
17
17.
Find the points on x-axis,
which are at a distance of
5
units
from the point
(
6
,
2
)
(i)
(
(
4
+
√
21
)
,
(
−
2
)
)
,
(
(
6
−
√
21
)
,
0
)
(ii)
(
(
6
+
√
21
)
,
0
)
,
(
(
6
−
√
21
)
,
0
)
(iii)
(
(
6
+
√
21
)
,
0
)
,
(
(
5
−
√
21
)
,
1
)
(iv)
(
(
7
+
√
21
)
,
(
−
1
)
)
,
(
(
6
−
√
21
)
,
0
)
(v)
(
(
8
+
√
21
)
,
2
)
,
(
(
6
−
√
21
)
,
0
)
Question
18
18.
If point P(x,y) lies in the third quadrant, then
(i)
x is positive and y is negative
(ii)
x is positive and y is positive
(iii)
x is negative and y is negative
(iv)
x is negative and y is positive
Question
19
19.
Find the ratio in which point
(
(
−
16
7
)
,
(
−
22
7
)
)
divides the join of points
(
(
−
8
)
,
2
)
and
(
2
,
(
−
7
)
)
(i)
9
:
6
(ii)
8
:
6
(iii)
8
:
9
(iv)
8
:
4
(v)
7
:
6
Question
20
20.
Find the point that bisects
(
7
,
(
−
6
)
)
and
(
6
,
1
)
(i)
(
11
2
,
(
−
3
2
)
)
(ii)
(
13
2
,
(
−
5
2
)
)
(iii)
(
9
2
,
(
−
9
2
)
)
(iv)
(
15
2
,
(
−
7
2
)
)
(v)
(
17
2
,
(
−
1
2
)
)
Question
21
21.
Find the coordinates of the vertices of the triangle,
the mid points of whose sides are
(
(
−
1
2
)
,
0
)
,
(
(
−
11
2
)
,
(
−
6
)
)
and
(
0
,
2
)
(i)
(
5
,
8
)
,
(
(
−
6
)
,
(
−
8
)
)
,
(
(
−
4
)
,
(
−
5
)
)
(ii)
(
5
,
8
)
,
(
(
−
4
)
,
(
−
6
)
)
,
(
(
−
5
)
,
(
−
4
)
)
(iii)
(
5
,
8
)
,
(
(
−
6
)
,
(
−
8
)
)
,
(
(
−
7
)
,
(
−
6
)
)
(iv)
(
5
,
8
)
,
(
(
−
6
)
,
(
−
8
)
)
,
(
(
−
5
)
,
(
−
4
)
)
(v)
(
4
,
9
)
,
(
(
−
6
)
,
(
−
8
)
)
,
(
(
−
5
)
,
(
−
4
)
)
Question
22
22.
If point P(x,y) lies in the first quadrant, then
(i)
x is positive and y is negative
(ii)
x is negative and y is positive
(iii)
x is negative and y is negative
(iv)
x is positive and y is positive
Question
23
23.
Determine the coordinates of point Q in the diagram.
(i)
(
(
−
7
)
,
(
−
8
)
)
(ii)
(
8
,
(
−
7
)
)
(iii)
(
(
−
8
)
,
7
)
(iv)
(
8
,
7
)
(v)
(
(
−
8
)
,
(
−
7
)
)
Question
24
24.
Which of the following equations satisfy the given points
(
(
−
2
)
,
86
11
)
,
(
(
−
1
)
,
76
11
)
,
(
0
,
6
)
,
(
1
,
56
11
)
,
(
2
,
46
11
)
?
(i)
(
−
10
x
−
11
y
+
69
)
=
0
(ii)
x
=
0
(iii)
y
=
(
−
10
11
x
+
6
)
(iv)
x
=
(
10
11
y
−
60
11
)
(v)
(
2
x
+
6
y
−
1
)
=
0
Question
25
25.
A and B are two points on the x-axis and y-axis respectively.
If
(
0
,
2
)
is the mid-point of the join of A and B, find A and B
(i)
(
0
,
0
)
,
(
(
−
1
)
,
5
)
(ii)
(
1
,
(
−
1
)
)
,
(
0
,
4
)
(iii)
(
0
,
0
)
,
(
0
,
4
)
(iv)
(
2
,
2
)
,
(
0
,
4
)
(v)
(
(
−
2
)
,
(
−
2
)
)
,
(
0
,
4
)
Assignment Key
1) (ii)
2) (i)
3) (v)
4) (iii)
5) (iii)
6) (i)
7) (iv)
8) (iv)
9) (i)
10) (iv)
11) (ii)
12) (iv)
13) (v)
14) (ii)
15) (ii)
16) (iv)
17) (ii)
18) (iii)
19) (ii)
20) (ii)
21) (iv)
22) (iv)
23) (v)
24) (iii)
25) (iii)
