Olympiad Mathematics - Co-ordinate Geometry
Exam Duration: 45 Mins Total Questions : 30
Where does the point (-2,0) lie?
- (a)
On positive X-axis.
- (b)
On positive Y-axis
- (c)
On negative X-axis.
- (d)
On negative Y-axis.
Where does the point (3,0) lie?
- (a)
On positve X-axis.
- (b)
On positive Y-axis.
- (c)
On negative X-axis.
- (d)
On negative Y-axis.
The points P(3, p) and Q(q, 5) represent the same point R. What are the respective values of p and q?
- (a)
5 and 3
- (b)
-5 and 3
- (c)
3 and 5
- (d)
3 and-5
What is the distance of a point (0,-3) from the origin?
- (a)
0 units
- (b)
-3 units
- (c)
cannot be determined
- (d)
3 units
Observe the given coordinate plane and answer the following questions.
What are the coordinates of point C?
- (a)
(0,0)
- (b)
(-1, 5)
- (c)
(2, -3)
- (d)
(4,2)
Observe the given coordinate plane and answer the following questions.
What are the coordinates of point E?
- (a)
(0, -2)
- (b)
(1, -2)
- (c)
(-2, 1)
- (d)
(-2,0)
Observe the given coordinate plane and answer the following questions.
What are the coordinates of point D?
- (a)
(-4, -1)
- (b)
(4,2)
- (c)
(0,4)
- (d)
(-1,5)
Observe the given coordinate plane and answer the following questions.
What is the y-coordinate of point F?
- (a)
-3
- (b)
0
- (c)
4
- (d)
-2
The points A(-a, -a), B(a,-a) C(-a, a), D(-a, a) form a polygon.
Where does the origin lie?
- (a)
On the vertex of the polygon.
- (b)
On the side of the polygon.
- (c)
Outside the polygon.
- (d)
At the point where the diagonals of the polygon meet.
Observe the given coordinate plane and answer the following questions.
In which quadrant is the point (3, 3)?
- (a)
Q1
- (b)
Q2
- (c)
Q3
- (d)
Q4
Observe the given coordinate plane and answer the following questions.
Which point is represented by the ordered pair (-3, -1)?
- (a)
P
- (b)
Q
- (c)
R
- (d)
S
Observe the given coordinate plane and answer the following questions.
What are the coordinates of the point Q?
- (a)
(-2,2)
- (b)
(2,-2)
- (c)
(3,3)
- (d)
(-3, -1)
Which of the following quadrants has/have points with a positive abscissa?
- (a)
I and II quadrants
- (b)
I and IV quadrants
- (c)
I quadrant only
- (d)
IV quadrant only
Which of the following points lie on the y-axis?
- (a)
(0,4)
- (b)
(-2,0)
- (c)
(3,0)
- (d)
(-1,-1)
The perpendicular distance of a point from the x-axis is 4 units and its perpendicular distance from the y axis is 5 units. What are the coordinates of such a point if it lies in the II Quadrant?
- (a)
(-4,5)
- (b)
(-5,4)
- (c)
(-4, -5)
- (d)
(5,-4)
Which of the following points lie on x-axis?
A(0,2),B(0,6),C(-3,0),D(0,-3),E(0,4),F(6,0),G(3,0)
- (a)
C, E and F
- (b)
D, E and B
- (c)
C, H and F
- (d)
C, H and B
In the given graph,\(\triangle ABC\) and\(\triangle ABD\) are equilateral triangles.
Find the respective coordinates of points C and D.
- (a)
\((0,a\sqrt 3)(0,a\sqrt 3)\)
- (b)
\((0,-a\sqrt 3)(0,a\sqrt 3)\)
- (c)
\((0,a\sqrt 3)(0,-a\sqrt 3)\)
- (d)
\((a\sqrt 3,0)(-a\sqrt 3,0)\)
Which of the following are the signs of the coordinates of a point in the II quadrant?
- (a)
(+, +)
- (b)
(-,+)
- (c)
(-,-)
- (d)
(+.-)
Which of the following is true about the ordinate?
- (a)
It is positive above x-axis.
- (b)
It is positive above y-axis.
- (c)
It is positive to the right of the origin.
- (d)
It is negative to the left of the origin.
Which figure is formed by joining points O(0,0), B(16,0)and C(16,12)on a graph paper?
- (a)
A triangle
- (b)
A square
- (c)
A right-angled triangle
- (d)
A line
Which of the following graph represents the point P(-a, b) where a < 0, b < 0?
- (a)
- (b)
- (c)
- (d)
The perpendicular distance of a point from the x-axis is 4 units and its perpendicular distance from the y-axis is 5 units. What are the coordinates of such a point if it lies in the II Quadrant?
- (a)
(-4,5)
- (b)
(-5,4)
- (c)
(-4, -5)
- (d)
(5,-4)
(2, 1) is a point, which belongs to the line ________.
- (a)
x = Y
- (b)
Y = x + 1
- (c)
2y = x
- (d)
xy = 1
One set of ordered pair which belongs to a straight line represented by an equation y = 2x - 1 is _________.
- (a)
(1,1)
- (b)
(2,1)
- (c)
(1,2)
- (d)
(3,1)
The coordinate axes divide the plane into _______.
- (a)
One part
- (b)
Two parts
- (c)
Three parts
- (d)
Four parts
If (x + 3, 5) = (2, 2 - y) then the values of the x and y respectively are
- (a)
5,3
- (b)
-1,-3
- (c)
0, -3
- (d)
1, 3
State 'T' for true and 'F' for false.
(i) Origin is the only point which lies on both the axes.
(ii) The point (2, -2) and point (-2, 2) lies in the same quadrant.
(iii) A point lies on y-axis at a distance 2 units from x-axis then it's coordinates are (2, 0).
(iv) Abscissa of a point is positive in I quadrant and also in II quadrant.
- (a)
i ii iii iv F T F T - (b)
i ii iii iv T F F F - (c)
i ii iii iv F T T F - (d)
i ii iii iv T F T F
In the given figure, PQRS is a rhombus whose diagonal PR and OS are along coordinate axis and PR = 12 units and QS = 6 units. Now, if T is a point which is 5 spaces right and 2 spaces above S. Find:
(i) sum of abscissae of P and T.
(ii) sum of ordinates of 0, Rand T.
- (a)
i ii -1 2 - (b)
i ii 1- 2 - (c)
i ii 1 2 - (d)
i ii -1 -2
In the given figure, PORS is a rectangle with its centre at origin and length PQ = 2a units and breadth QR = 2b units. Find coordinates of all of its vertices.
- (a)
P(a, - b), Q(a, b), R(-a, b), S(-a, -b)
- (b)
P(a, - b), Q(a, b), R(a, - b), S(-a, -b)
- (c)
P(-a, b), Q(a, b), R(a, - b), S(-a, - b)
- (d)
P(-a, b), Q(a, b), R(a, - b), S(-a, b)
Match the following.
| Column-I | Column-II |
| (P) The area of \(\Delta\)OAB with 0(0,0), A (4, 0) and a (0, 8) is | (i) 14 sq. units |
| (Q) The area \(\Delta\)ABC with A (2, 0), a (6,0) and C (4, 6) is | (ii) 16 sq. units |
| (R) The area of \(\Delta\)OAB with 0(0,0), A (7, 0) and a (0, 4) is | (iii) 12 sq. units |
- (a)
(P) \(\rightarrow\) (ii), (Q) \(\rightarrow\) (i), (R) \(\rightarrow\) (iii)
- (b)
(P) \(\rightarrow\) (iii), (Q) \(\rightarrow\) (i), (R) \(\rightarrow\) (ii)
- (c)
(P) \(\rightarrow\) (iii), (Q) \(\rightarrow\) (ii), (R) \(\rightarrow\) (i)
- (d)
(P)\(\rightarrow\)(ii), (Q) \(\rightarrow\) (iii), (R) \(\rightarrow\) (i)
