EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Coordinate Geometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
If point P
(x,4)
is equidistant from the points
(
(
−
3
)
,
5
)
and
(
2
,
3
)
, find x
(i)
(
-3
2
)
(ii)
1
2
(iii)
-1
(iv)
(
-1
2
)
(v)
(
-1
4
)
Question
2
2.
Which of the following sets of points are collinear?
(i)
(
(
−
1
)
,
5
)
,
(
0
,
2
)
,
(
1
,
(
−
6
)
)
(ii)
(
4
,
(
−
7
)
)
,
(
0
,
(
−
7
)
)
,
(
(
−
5
)
,
(
−
1
)
)
(iii)
(
7
,
0
)
,
(
(
−
5
)
,
(
−
1
)
)
,
(
(
−
3
)
,
0
)
(iv)
(
8
,
5
)
,
(
3
,
4
)
,
(
1
,
18
5
)
(v)
(
(
−
5
)
,
(
−
7
)
)
,
(
7
,
7
)
,
(
7
,
(
−
3
)
)
Question
3
3.
In what ratio is the join of
(
5
,
3
)
and
(
(
−
6
)
,
(
−
8
)
)
divided by y-axis?
(i)
8
:
2
(ii)
5
:
9
(iii)
5
:
6
(iv)
5
:
3
(v)
6
:
2
Question
4
4.
Three vertices of a parallelogram are
(
(
−
3
)
,
(
−
5
)
)
,
(
5
,
(
−
5
)
)
and
(
8
,
0
)
.
Find the fourth vertex
(i)
(
(
−
1
)
,
1
)
(ii)
(
2
,
2
)
(iii)
(
0
,
0
)
(iv)
(
1
,
(
−
1
)
)
(v)
(
(
−
2
)
,
(
−
2
)
)
Question
5
5.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
0
,
7
)
and
(
1
,
8
)
(i)
(
−
13
x
−
6
y
+
21
)
=
0
(ii)
(
x
+
y
−
8
)
=
0
(iii)
(
−
13
x
−
3
y
+
21
)
=
0
(iv)
(
y
−
8
)
=
0
(v)
(
x
+
3
y
−
8
)
=
0
Question
6
6.
Find the point on y-axis which is equidistant
from the points
(
(
−
6
)
,
(
−
2
)
)
and
(
(
−
5
)
,
5
)
(i)
(
(
−
1
)
,
12
7
)
(ii)
(
(
−
2
)
,
(
−
9
7
)
)
(iii)
(
2
,
19
7
)
(iv)
(
0
,
5
7
)
(v)
(
1
,
(
−
2
7
)
)
Question
7
7.
The points
(
(
−
3
)
,
(
−
3
)
)
,
(
1
,
1
)
and
(
5
,
(
−
3
)
)
represent
(i)
collinear points
(ii)
scalene triangle
(iii)
equilateral triangle
(iv)
right angle triangle
(v)
isosceles right angled triangle
Question
8
8.
Find the coordinates of the vertices of the triangle,
the mid points of whose sides are
(
(
−
7
2
)
,
3
2
)
,
(
(
−
7
2
)
,
(
−
5
2
)
)
and
(
(
−
4
)
,
0
)
(i)
(
(
−
4
)
,
4
)
,
(
(
−
3
)
,
(
−
1
)
)
,
(
(
−
6
)
,
(
−
6
)
)
(ii)
(
(
−
5
)
,
5
)
,
(
(
−
3
)
,
(
−
1
)
)
,
(
(
−
4
)
,
(
−
4
)
)
(iii)
(
(
−
4
)
,
4
)
,
(
(
−
3
)
,
(
−
1
)
)
,
(
(
−
4
)
,
(
−
4
)
)
(iv)
(
(
−
4
)
,
4
)
,
(
(
−
3
)
,
(
−
1
)
)
,
(
(
−
3
)
,
(
−
5
)
)
(v)
(
(
−
4
)
,
4
)
,
(
(
−
1
)
,
1
)
,
(
(
−
4
)
,
(
−
4
)
)
Question
9
9.
The points
(
(
−
2
)
,
4
)
,
(
(
−
5
)
,
0
)
and
(
(
−
7
2
+
2
√
3
)
,
(
2
−
3
2
√
3
)
)
represent
(i)
scalene triangle
(ii)
equilateral triangle
(iii)
isosceles triangle
(iv)
right angled triangle
Question
10
10.
Find the lengths of the medians of a triangle whose vertices are
(
(
−
5
)
,
(
−
5
)
)
,
(
(
−
3
)
,
(
−
2
)
)
and
(
6
,
8
)
(i)
5
2
√
17
,
7
2
√
2
,
1
2
√
929
(ii)
1
2
√
181
,
1
2
√
290
,
1
2
√
13
(iii)
1
2
√
13
,
1
2
√
181
,
1
2
√
181
Question
11
11.
Find the point that bisects
(
4
,
1
)
and
(
(
−
5
)
,
8
)
(i)
(
(
−
1
2
)
,
9
2
)
(ii)
(
3
2
,
13
2
)
(iii)
(
(
−
3
2
)
,
11
2
)
(iv)
(
(
−
5
2
)
,
5
2
)
(v)
(
1
2
,
7
2
)
Question
12
12.
The points
(
4
,
7
)
,
(
(
−
4
)
,
(
−
7
)
)
and
(
3
2
,
21
8
)
represents
(i)
collinear points
(ii)
isoceles triangle
(iii)
right angle triangle
(iv)
equilateral triangle
Question
13
13.
The mid-point of the join of the points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is
(i)
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
(ii)
(
x
1
−
x
2
3
,
y
1
−
y
2
3
)
(iii)
(
y
1
−
y
2
2
,
x
1
−
x
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
14
14.
Distance of the given point from y-axis is
(i)
3
(ii)
7
(iii)
4
(iv)
-1
(v)
12
Question
15
15.
Find the lengths of the sides of the triangle formed by the points
(
0
,
(
−
3
)
)
,
(
5
,
6
)
and
(
(
−
8
)
,
8
)
(i)
√
106
,
√
173
,
√
187
(ii)
√
106
,
173
,
√
185
(iii)
4
√
106
,
√
173
,
√
185
(iv)
√
106
,
√
173
,
√
185
Question
16
16.
Find the value of k such that the points
(
(
−
4
)
,
(
−
2
)
)
,
(
(
−
2
3
)
,
8
3
)
and
(k,5)
are collinear
(i)
3
(ii)
0
(iii)
2
(iv)
1
(v)
-2
Question
17
17.
The points
(
(
−
2
)
,
(
−
1
)
)
,
(
5
,
(
−
1
)
)
,
(
9
,
4
)
and
(
2
,
4
)
represent
(i)
square
(ii)
trapezium
(iii)
rhombus
(iv)
rectangle
(v)
parallelogram
Question
18
18.
The points
(
(
−
6
)
,
(
−
5
)
)
,
(
2
,
(
−
5
)
)
,
(
2
,
(
−
1
)
)
and
(
(
−
6
)
,
(
−
1
)
)
represents
(i)
rectangle
(ii)
parallelogram
(iii)
rhombus
(iv)
square
(v)
trapezium
Question
19
19.
KM is the straight line of length
√
61
units.
If K has the coordinates
(
(
−
3
)
,
1
)
and M has coordinates
(k,7)
,
find the possible values of k
(i)
(
2
,
(
−
8
)
)
(ii)
(
0
,
(
−
10
)
)
(iii)
(
3
,
(
−
9
)
)
(iv)
(
1
,
(
−
7
)
)
(v)
(
4
,
(
−
6
)
)
Question
20
20.
A point lies on negative side of y-axis at a distance of 5 units from x-axis. What are the coordinates of the point?
(i)
(
5
,
0
)
(ii)
(
(
−
5
)
,
0
)
(iii)
(
0
,
(
−
5
)
)
(iv)
(
0
,
5
)
Question
21
21.
Find the area of the triangle
formed by the points
(
(
−
3
)
,
(
−
6
)
)
,
(
(
−
2
)
,
1
)
and
(
(
−
3
)
,
4
)
(i)
4
(ii)
2
(iii)
7
(iv)
6
(v)
5
Question
22
22.
Distance of the point (9,2) from x-axis is
(i)
9
(ii)
(
−
7
)
(iii)
2
(iv)
11
(v)
7
Question
23
23.
The points
(
(
−
5
)
,
(
−
2
)
)
,
(
2
,
(
−
5
)
)
,
(
9
,
(
−
2
)
)
and
(
2
,
1
)
represent
(i)
rhombus
(ii)
trapezium
(iii)
rectangle
(iv)
square
(v)
parallelogram
Question
24
24.
A point lies on negative side of x-axis at a distance of 4 units from y-axis. What are the coordinates of the point?
(i)
(
(
−
4
)
,
0
)
(ii)
(
0
,
4
)
(iii)
(
0
,
(
−
4
)
)
(iv)
(
4
,
0
)
Question
25
25.
The centre of a circle is
(
(
−
1
2
)
,
9
2
)
.
Find the other end of the diameter whose one end point is
(
(
−
4
)
,
8
)
(i)
(
3
,
(
−
1
)
)
(ii)
(
(
−
3
)
,
(
−
1
)
)
(iii)
(
3
,
1
)
(iv)
(
(
−
3
)
,
1
)
(v)
(
1
,
3
)
Assignment Key
1) (iv)
2) (iv)
3) (iii)
4) (iii)
5) (ii)
6) (iv)
7) (v)
8) (iii)
9) (ii)
10) (i)
11) (i)
12) (i)
13) (i)
14) (i)
15) (iv)
16) (iv)
17) (v)
18) (i)
19) (i)
20) (iii)
21) (v)
22) (iii)
23) (i)
24) (i)
25) (iii)
