EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Coordinate Geometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Find the point on x-axis which is equidistant
from the points
(
(
−
5
)
,
(
−
1
)
)
and
(
3
,
(
−
4
)
)
(i)
(
31
16
,
2
)
(ii)
(
(
−
33
16
)
,
(
−
2
)
)
(iii)
(
15
16
,
(
−
1
)
)
(iv)
(
(
−
17
16
)
,
1
)
(v)
(
(
−
1
16
)
,
0
)
Question
2
2.
A point lies on positive side of y-axis at a distance of 2 units from x-axis. What are the coordinates of the point?
(i)
(
2
,
0
)
(ii)
(
0
,
2
)
(iii)
(
0
,
(
−
2
)
)
(iv)
(
(
−
2
)
,
0
)
Question
3
3.
The points
(
5
,
(
−
8
)
)
,
(
(
−
5
)
,
8
)
and
(
(
−
45
19
)
,
72
19
)
represents
(i)
collinear points
(ii)
equilateral triangle
(iii)
right angle triangle
(iv)
isoceles triangle
Question
4
4.
Distance of the given point from y-axis is
(i)
5
(ii)
8
(iii)
3
(iv)
11
(v)
24
Question
5
5.
Find the area of the triangle
formed by the points
(
4
,
6
)
,
(
(
−
1
)
,
5
)
and
(
0
,
(
−
2
)
)
(i)
20
(ii)
16
(iii)
17
(iv)
18
(v)
19
Question
6
6.
Find the lengths of the medians of a triangle whose vertices are
(
4
,
0
)
,
(
1
,
(
−
2
)
)
and
(
(
−
4
)
,
(
−
5
)
)
(i)
1
2
√
13
,
1
2
√
34
,
1
2
√
34
(ii)
1
2
√
170
,
1
2
√
5
,
1
2
√
233
(iii)
1
2
√
34
,
1
2
√
89
,
1
2
√
13
Question
7
7.
Find the coordinates of the midpoints of the sides of the quadrilateral
formed by
(
(
−
1
)
,
(
−
3
)
)
,
(
3
,
2
)
,
(
(
−
2
)
,
3
)
and
(
(
−
3
)
,
3
)
(i)
(
1
,
(
−
1
2
)
)
,
(
1
2
,
5
2
)
,
(
(
−
5
2
)
,
3
)
,
(
(
−
3
)
,
1
)
(ii)
(
1
,
(
−
1
2
)
)
,
(
1
2
,
5
2
)
,
(
(
−
5
2
)
,
3
)
,
(
(
−
2
)
,
0
)
(iii)
(
1
,
(
−
1
2
)
)
,
(
1
2
,
5
2
)
,
(
(
−
9
2
)
,
1
)
,
(
(
−
2
)
,
0
)
(iv)
(
3
,
3
2
)
,
(
1
2
,
5
2
)
,
(
(
−
5
2
)
,
3
)
,
(
(
−
2
)
,
0
)
(v)
(
1
,
(
−
1
2
)
)
,
(
1
2
,
5
2
)
,
(
(
−
3
2
)
,
2
)
,
(
(
−
2
)
,
0
)
Question
8
8.
The points
(
(
−
4
)
,
(
−
2
)
)
,
(
0
,
2
)
,
(
4
,
(
−
2
)
)
and
(
0
,
(
−
6
)
)
represent
(i)
trapezium
(ii)
rectangle
(iii)
rhombus
(iv)
square
(v)
parallelogram
Question
9
9.
A and B are two points on the x-axis and y-axis respectively.
If
(
(
−
7
)
,
(
−
5
)
)
is the mid-point of the join of A and B, find A and B
(i)
(
(
−
14
)
,
0
)
,
(
0
,
(
−
10
)
)
(ii)
(
(
−
14
)
,
0
)
,
(
(
−
1
)
,
(
−
9
)
)
(iii)
(
(
−
13
)
,
(
−
1
)
)
,
(
0
,
(
−
10
)
)
(iv)
(
(
−
16
)
,
(
−
2
)
)
,
(
0
,
(
−
10
)
)
(v)
(
(
−
12
)
,
2
)
,
(
0
,
(
−
10
)
)
Question
10
10.
Find the distance between the points
(
(
−
2
)
,
8
)
and
(
8
,
(
−
2
)
)
(i)
20
(ii)
10
√
4
(iii)
10
4
√
2
(iv)
10
√
1
2
(v)
10
√
2
Question
11
11.
The points
(
(
−
4
)
,
(
−
5
)
)
,
(
3
,
(
−
5
)
)
,
(
3
,
0
)
and
(
(
−
4
)
,
0
)
represents
(i)
rectangle
(ii)
trapezium
(iii)
rhombus
(iv)
square
(v)
parallelogram
Question
12
12.
Find the point that bisects
(
3
,
(
−
2
)
)
and
(
5
,
6
)
(i)
(
3
,
3
)
(ii)
(
2
,
0
)
(iii)
(
4
,
2
)
(iv)
(
5
,
1
)
(v)
(
6
,
4
)
Question
13
13.
Find the lengths of the sides of the triangle formed by the points
(
(
−
7
)
,
2
)
,
(
3
,
(
−
1
)
)
and
(
6
,
(
−
5
)
)
(i)
√
109
,
5
,
√
221
(ii)
4
√
109
,
5
,
√
218
(iii)
√
109
,
5
,
√
218
(iv)
√
109
,
4
,
√
218
Question
14
14.
If point P
(
(
−
5
7
)
,
3
)
is equidistant from the points
(a,7)
and
(
(
−
7
)
,
(
−
3
)
)
, find a
(i)
4
(ii)
8
(iii)
7
(iv)
9
(v)
6
Question
15
15.
In what ratio is the join of
(
(
−
3
)
,
4
)
and
(
1
,
(
−
7
)
)
divided by x-axis?
(i)
1
:
7
(ii)
4
:
7
(iii)
3
:
7
(iv)
5
:
7
(v)
1
:
3
Question
16
16.
Find the centre of the circle, the endpoints of whose
diameter are
(
(
−
6
)
,
7
)
and
(
(
−
4
)
,
7
)
(i)
(
5
,
(
−
7
)
)
(ii)
(
7
,
(
−
5
)
)
(iii)
(
(
−
5
)
,
(
−
7
)
)
(iv)
(
5
,
7
)
(v)
(
(
−
5
)
,
7
)
Question
17
17.
A point lies on negative side of x-axis at a distance of 6 units from y-axis. What are the coordinates of the point?
(i)
(
6
,
0
)
(ii)
(
0
,
(
−
6
)
)
(iii)
(
0
,
6
)
(iv)
(
(
−
6
)
,
0
)
Question
18
18.
Distance of the point (6,5) from x-axis is
(i)
5
(ii)
(
−
1
)
(iii)
6
(iv)
1
(v)
11
Question
19
19.
Find the coordinates of the mid points of the sides of the triangle formed by
(
(
−
2
)
,
(
−
7
)
)
,
(
2
,
1
)
and
(
(
−
4
)
,
(
−
2
)
)
(i)
(
0
,
(
−
3
)
)
,
(
(
−
1
)
,
(
−
1
2
)
)
,
(
(
−
3
)
,
(
−
9
2
)
)
(ii)
(
0
,
(
−
3
)
)
,
(
(
−
1
)
,
(
−
1
2
)
)
,
(
(
−
2
)
,
(
−
11
2
)
)
(iii)
(
0
,
(
−
3
)
)
,
(
(
−
1
)
,
(
−
1
2
)
)
,
(
(
−
5
)
,
(
−
13
2
)
)
(iv)
(
(
−
1
)
,
(
−
2
)
)
,
(
(
−
1
)
,
(
−
1
2
)
)
,
(
(
−
3
)
,
(
−
9
2
)
)
(v)
(
0
,
(
−
3
)
)
,
(
1
,
3
2
)
,
(
(
−
3
)
,
(
−
9
2
)
)
Question
20
20.
The points
(
7
,
(
−
1
)
)
,
(
3
,
6
)
and
(
(
5
−
7
2
√
3
)
,
(
5
2
−
2
√
3
)
)
represent
(i)
isosceles triangle
(ii)
equilateral triangle
(iii)
scalene triangle
(iv)
right angled triangle
Question
21
21.
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)
(
m
x
2
−
n
x
1
m - n
,
m
y
2
−
n
y
1
m - n
)
(ii)
(
n
x
2
−
m
x
1
m - n
,
n
y
2
−
m
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
22
22.
In what ratio is the join of
(
6
,
(
−
2
)
)
and
(
(
−
1
)
,
8
)
divided by y-axis?
(i)
6
:
-1
(ii)
6
:
1
(iii)
2
:
1
(iv)
0
:
1
(v)
6
:
4
Question
23
23.
If point P
(x,4)
is equidistant from the points
(
(
−
1
)
,
(
−
8
)
)
and
(
6
,
(
−
4
)
)
, find x
(i)
(
-13
4
)
(ii)
(
-51
16
)
(iii)
(
-47
14
)
(iv)
(
-45
14
)
(v)
(
-43
14
)
Question
24
24.
One end of the diameter of a circle is
(
(
−
5
)
,
8
)
.
If the centre is
(
(
−
2
)
,
1
)
,
find the other end of the diameter
(i)
(
3
,
(
−
4
)
)
(ii)
(
0
,
(
−
5
)
)
(iii)
(
1
,
(
−
6
)
)
(iv)
(
2
,
(
−
7
)
)
(v)
(
(
−
1
)
,
(
−
8
)
)
Question
25
25.
Three vertices of a parallelogram are
(
(
−
2
)
,
(
−
4
)
)
,
(
5
,
(
−
4
)
)
and
(
8
,
0
)
.
Find the fourth vertex
(i)
(
(
−
1
)
,
(
−
2
)
)
(ii)
(
2
,
(
−
1
)
)
(iii)
(
1
,
0
)
(iv)
(
3
,
2
)
(v)
(
0
,
1
)
Assignment Key
1) (v)
2) (ii)
3) (i)
4) (ii)
5) (iv)
6) (ii)
7) (ii)
8) (iv)
9) (i)
10) (v)
11) (i)
12) (iii)
13) (iii)
14) (iii)
15) (ii)
16) (v)
17) (iv)
18) (i)
19) (i)
20) (ii)
21) (iii)
22) (ii)
23) (iv)
24) (iii)
25) (iii)
