EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Coordinate Geometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Some volunteers on a cleanliness drive decided to clean an open ground in the shape of a quadrilateral ABCD, where AB = 18.00 m, BC = 16.00 m, CD = 16.00 m, and DA = 11.00 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 49 m. Which group cleaned more area ? Find the total area cleaned by both groups.
(i)
group n
,
229.30 sq.m
(ii)
group m
,
210.30 sq.m
(iii)
group m
,
235.30 sq.m
(iv)
group n
,
223.30 sq.m
Question
2
2.
Which of the points (4,4), (-3,7), (-6,-9) and (3,-2) belong to the first quadrant?
(i)
(
(
−
3
)
,
7
)
(ii)
(
(
−
6
)
,
(
−
9
)
)
(iii)
(
3
,
(
−
2
)
)
(iv)
(
4
,
4
)
Question
3
3.
The centre of a circle is
(
3
2
,
(
−
7
2
)
)
.
Find the other end of the diameter whose one end point is
(
6
,
(
−
8
)
)
(i)
(
3
,
(
−
1
)
)
(ii)
(
1
,
(
−
3
)
)
(iii)
(
3
,
1
)
(iv)
(
(
−
3
)
,
(
−
1
)
)
(v)
(
(
−
3
)
,
1
)
Question
4
4.
Three vertices of a parallelogram are
(
(
−
2
)
,
(
−
3
)
)
,
(
5
,
(
−
3
)
)
and
(
9
,
0
)
.
Find the fourth vertex
(i)
(
2
,
0
)
(ii)
(
4
,
2
)
(iii)
(
1
,
1
)
(iv)
(
0
,
(
−
2
)
)
(v)
(
3
,
(
−
1
)
)
Question
5
5.
If point P(x,y) lies in the second quadrant, then
(i)
x is negative and y is negative
(ii)
x is negative and y is positive
(iii)
x is positive and y is negative
(iv)
x is positive and y is positive
Question
6
6.
Find the area of the triangle
formed by the points
(
(
−
5
)
,
6
)
,
(
(
−
1
)
,
6
)
and
(
(
−
1
)
,
3
)
(i)
7
(ii)
5
(iii)
8
(iv)
3
(v)
6
Question
7
7.
If point P
(x,7)
is equidistant from the points
(
6
,
4
)
and
(
(
−
4
)
,
6
)
, find x
(i)
7
5
(ii)
1
(iii)
9
7
(iv)
9
5
(v)
5
3
Question
8
8.
The coordinates of a point which is 5 units away from x-axis and 3 units away from y-axis in the fourth quadrant is
(i)
(
3
,
(
−
5
)
)
(ii)
(
(
−
3
)
,
(
−
5
)
)
(iii)
(
(
−
3
)
,
5
)
(iv)
(
3
,
5
)
(v)
(
(
−
5
)
,
3
)
Question
9
9.
Determine the coordinates of point L in the diagram.
(i)
(
6
,
4
)
(ii)
(
(
−
6
)
,
(
−
4
)
)
(iii)
(
4
,
6
)
(iv)
(
(
−
6
)
,
4
)
(v)
(
6
,
(
−
4
)
)
Question
10
10.
Find the lengths of the medians of a triangle whose vertices are
(
(
−
6
)
,
4
)
,
(
(
−
3
)
,
(
−
1
)
)
and
(
3
,
(
−
6
)
)
(i)
3
2
√
41
,
3
2
,
15
2
√
2
(ii)
1
2
√
61
,
1
2
√
181
,
1
2
√
34
(iii)
1
2
√
34
,
1
2
√
61
,
1
2
√
61
Question
11
11.
Which of the following is a point on the positive x-axis?
(i)
(
4
,
0
)
(ii)
(
0
,
7
)
(iii)
(
0
,
(
−
4
)
)
(iv)
(
(
−
6
)
,
0
)
(v)
(
(
−
3
)
,
3
)
Question
12
12.
If point P
(
(
−
39
5
)
,
4
)
is equidistant from the points
(a,-1)
and
(
(
−
8
)
,
(
−
7
)
)
, find a
(i)
1
(ii)
5
(iii)
3
(iv)
0
(v)
2
Question
13
13.
Which of the following is a point on the positive y-axis?
(i)
(
(
−
3
)
,
8
)
(ii)
(
0
,
2
)
(iii)
(
(
−
3
)
,
0
)
(iv)
(
2
,
0
)
(v)
(
0
,
(
−
3
)
)
Question
14
14.
A line which is neither parallel to x-axis nor y-axis is
(i)
a vertical line
(ii)
a curved line
(iii)
a horizontal line
(iv)
an oblique line
Question
15
15.
Find the point that divides the join of points
(
7
,
(
−
7
)
)
and
(
1
,
4
)
internally
in the ratio
9
:
3
(i)
(
7
2
,
1
4
)
(ii)
(
1
2
,
(
−
3
4
)
)
(iii)
(
5
2
,
5
4
)
(iv)
(
9
2
,
13
4
)
(v)
(
3
2
,
9
4
)
Question
16
16.
If A
(
(
−
2
)
,
(
−
6
)
)
and B
(
(
−
8
)
,
7
)
are two points,
find the coordinates of the point C on AB produced so that AC = 2BC
(i)
(
(
−
14
)
,
20
)
(ii)
(
(
−
16
)
,
18
)
(iii)
(
(
−
13
)
,
19
)
(iv)
(
(
−
15
)
,
21
)
(v)
(
(
−
12
)
,
22
)
Question
17
17.
Find the distance between the points
(
(
−
2
)
,
(
−
1
)
)
and
(
(
−
1
)
,
5
)
(i)
√
39
(ii)
√
37
(iii)
37
(iv)
√
35
(v)
4
√
37
Question
18
18.
The mid-point of the join of the points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is
(i)
(
y
1
−
y
2
2
,
x
1
−
x
2
2
)
(ii)
(
x
1
−
x
2
3
,
y
1
−
y
2
3
)
(iii)
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
(iv)
(
x
1
+
x
2
3
,
y
1
+
y
2
3
)
(v)
(
x
1
−
x
2
2
,
y
1
−
y
2
2
)
Question
19
19.
The point
(
(
−
8
)
,
9
)
lies in
(i)
third quadrant
(ii)
fourth quadrant
(iii)
first quadrant
(iv)
second quadrant
Question
20
20.
A point lies on positive side of y-axis at a distance of 4 units from x-axis. What are the coordinates of the point?
(i)
(
(
−
4
)
,
0
)
(ii)
(
0
,
(
−
4
)
)
(iii)
(
0
,
4
)
(iv)
(
4
,
0
)
Question
21
21.
Find the set of points satisfying the equation
(
9
x
+
15
y
−
5
)
=
0
(i)
(
(
−
2
)
,
23
15
)
,
(
(
−
1
)
,
14
15
)
,
(
0
,
1
3
)
,
(
1
,
(
−
4
15
)
)
,
(
2
,
(
−
13
15
)
)
(ii)
(
(
−
2
)
,
23
15
)
,
(
(
−
1
)
,
14
15
)
,
(
(
−
2
)
,
(
−
5
3
)
)
,
(
1
,
(
−
4
15
)
)
,
(
2
,
(
−
13
15
)
)
(iii)
(
(
−
2
)
,
23
15
)
,
(
(
−
1
)
,
14
15
)
,
(
0
,
1
3
)
,
(
1
,
(
−
4
15
)
)
,
(
4
,
17
15
)
(iv)
(
(
−
2
)
,
23
15
)
,
(
(
−
1
)
,
14
15
)
,
(
0
,
1
3
)
,
(
0
,
11
15
)
,
(
2
,
(
−
13
15
)
)
(v)
(
(
−
2
)
,
23
15
)
,
(
(
−
1
)
,
14
15
)
,
(
1
,
(
−
2
3
)
)
,
(
1
,
(
−
4
15
)
)
,
(
2
,
(
−
13
15
)
)
Question
22
22.
Determine the coordinates of point H in the diagram.
(i)
(
8
,
3
)
(ii)
(
3
,
(
−
8
)
)
(iii)
(
8
,
(
−
3
)
)
(iv)
(
(
−
8
)
,
(
−
3
)
)
(v)
(
(
−
8
)
,
3
)
Question
23
23.
The coordinates of the point dividing the join of points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
internally in the ratio m:n are
(i)
(
n
x
2
−
m
x
1
m - n
,
n
y
2
−
m
y
1
m - n
)
(ii)
(
m
x
2
−
n
x
1
m - n
,
m
y
2
−
n
y
1
m - n
)
(iii)
(
m
x
2
+
n
x
1
m + n
,
m
y
2
+
n
y
1
m + n
)
(iv)
(
n
x
2
+
m
x
1
m + n
,
n
y
2
+
m
y
1
m + n
)
Question
24
24.
Which of the following equations satisfy the given points
(
(
−
2
)
,
10
3
)
,
(
(
−
1
)
,
2
)
,
(
0
,
2
3
)
,
(
1
,
(
−
2
3
)
)
,
(
2
,
(
−
2
)
)
?
(i)
x
=
(
−
5
)
(ii)
y
=
1
(iii)
(
4
x
+
3
y
−
2
)
=
0
(iv)
(
−
12
x
−
7
y
+
11
)
=
0
(v)
x
=
(
12
7
y
−
47
7
)
Question
25
25.
Which of the following lines pass through the origin?
(i)
(
3
x
−
4
y
)
=
0
(ii)
(
4
x
+
6
y
−
34
)
=
0
(iii)
(
x
−
14
y
−
63
)
=
0
(iv)
(
−
12
x
+
5
y
−
59
)
=
0
(v)
(
7
x
+
3
y
−
37
)
=
0
Assignment Key
1) (iv)
2) (iv)
3) (v)
4) (i)
5) (ii)
6) (v)
7) (i)
8) (i)
9) (i)
10) (i)
11) (i)
12) (v)
13) (ii)
14) (iv)
15) (iii)
16) (i)
17) (ii)
18) (iii)
19) (iv)
20) (iii)
21) (i)
22) (v)
23) (iii)
24) (iii)
25) (i)
