Point \( (-3, 5) \) lies in the
first quadrant
second quadrant
third quadrant
fourth quadrant
Signs of the abscissa and ordinate of a point in the second quadrant are respectively
+, +
-, -
-, +
+, -
Point \( (0, -7) \) lies
on the x-axis
in the second quadrant
on the y-axis
in the fourth quadrant
Point \( (-10, 0) \) lies
on the negative direction of the x-axis
on the negative direction of the y-axis
in the third quadrant
in the fourth quadrant
Abscissa of all the points on the x-axis is
0
1
2
any number
Ordinate of all points on the x-axis is
0
1
-1
any number
The point at which the two coordinate axes meet is called the
abscissa
ordinate
origin
quadrant
A point both of whose coordinates are negative will lie in
I quadrant
II quadrant
III quadrant
IV quadrant
Points \( (1, -1) \), \( (2, -2) \), \( (4, -5) \), \( (-3, -4) \)
lie in II quadrant
lie in III quadrant
lie in IV quadrant
do not lie in the same quadrant
If y coordinate of a point is zero, then this point always lies
in I quadrant
in II quadrant
on x-axis
on y-axis
The points \( (-5, 2) \) and \( (2, -5) \) lie in the
same quadrant
II and III quadrants, respectively
II and IV quadrants, respectively
IV and II quadrants, respectively
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has
x coordinate = -5
y coordinate = 5 only
y coordinate = -5 only
y coordinate = 5 or -5
On plotting the points O \( (0, 0) \), A \( (3, 0) \), B \( (3, 4) \), C \( (0, 4) \) and joining OA, AB, BC and CO which of the following figure is obtained?
Square
Rectangle
Trapezium
Rhombus
If P \( (-1, 1) \), Q \( (3, -4) \), R \( (1, -1) \), S \( (-2, -3) \) and T \( (-4, 4) \) are plotted on the graph paper, then the point(s) in the fourth quadrant are
P and T
Q and R
Only S
P and R
If the coordinates of the two points are P \( (-2, 3) \) and Q \( (-3, 5) \), then (abscissa of P) − (abscissa of Q) is
-5
1
-1
-2
If P \( (5, 1) \), Q \( (8, 0) \), R \( (0, 4) \), S \( (0, 5) \) and O \( (0, 0) \) are plotted on the graph paper, then the point(s) on the x-axis are
P and R
R and S
Only Q
Q and O
Abscissa of a point is positive in
I and II quadrants
I and IV quadrants
I quadrant only
II quadrant only
The points whose abscissa and ordinate have different signs will lie in
I and II quadrants
II and III quadrants
I and III quadrants
II and IV quadrants
In Fig. 3.1, coordinates of P are
\( (-4, 2) \)
\( (-2, 4) \)
\( (4, -2) \)
\( (2, -4) \)
In Fig. 3.2, the point identified by the coordinates \( (-5, 3) \) is
T
R
L
S
The point whose ordinate is 4 and which lies on y-axis is
\( (4, 0) \)
\( (0, 4) \)
\( (1, 4) \)
\( (4, 2) \)
Which of the points P\( (0, 3) \), Q\( (1, 0) \), R\( (0, -1) \), S\( (-5, 0) \), T\( (1, 2) \) do not lie on the x-axis?
P and R only
Q and S only
P, R and T
Q, S and T
The point which lies on y-axis at a distance of 5 units in the negative direction of y-axis is
\( (0, 5) \)
\( (5, 0) \)
\( (0, -5) \)
\( (-5, 0) \)
The perpendicular distance of the point P \( (3, 4) \) from the y-axis is
3
4
5
7
Write whether the following statements are True or False. Justify your answer.
(i) Point \((3, 0)\) lies in the first quadrant.
(ii) Points \((1, -1)\) and \((-1, 1)\) lie in the same quadrant.
(iii) The coordinates of a point whose ordinate is \(-\dfrac{1}{2}\) and abscissa is \(1\) are \((-\dfrac{1}{2}, 1)\).
(iv) A point lies on y-axis at a distance of 2 units from the x-axis. Its coordinates are \((2, 0)\).
(v) \((-1, 7)\) is a point in the II quadrant.
(i) False, because if ordinate of a point is zero, the point lies on the x-axis.
(ii) False. \((1, -1)\) lies in IV quadrant and \((-1, 1)\) lies in II quadrant.
(iii) False, because in the coordinates of a point abscissa comes first and then the ordinate.
(iv) False, because a point on the y-axis is of the form \((0, y)\).
(v) True, because in the II quadrant, signs of abscissa and ordinate are \(-\), \(+\), respectively.
Write the coordinates of each of the points P, Q, R, S, T and O from the Fig. 3.5.
\(P(1,1)\), \(Q(-3,0)\), \(R(-3,-2)\), \(S(2,1)\), \(T(4,-2)\), \(O(0,0)\)
Plot the following points and write the name of the figure obtained by joining them in order:
\(P(-3,2)\), \(Q(-7,-3)\), \(R(6,-3)\), \(S(2,2)\)
Trapezium
Plot the points \((x,y)\) given by the following table:
| \(x\) | 2 | 4 | -3 | -2 | 3 | 0 |
|---|---|---|---|---|---|---|
| \(y\) | 4 | 2 | 0 | 5 | -3 | 0 |
Plot the following points and check whether they are collinear or not:
(i) \((1,3)\), \((-1,-1)\), \((-2,-3)\)
(ii) \((1,1)\), \((2,-3)\), \((-1,-2)\)
(iii) \((0,0)\), \((2,2)\), \((5,5)\)
(i) Collinear
(ii) Not collinear
(iii) Collinear
Without plotting the points indicate the quadrant in which they will lie, if:
(i) ordinate is 5 and abscissa is -3
(ii) abscissa is -5 and ordinate is -3
(iii) abscissa is -5 and ordinate is 3
(iv) ordinate is 5 and abscissa is 3
(i) II
(ii) III
(iii) II
(iv) I
In Fig. 3.6, LM is a line parallel to the y-axis at a distance of 3 units.
(i) What are the coordinates of the points P, R and Q?
(ii) What is the difference between the abscissa of the points L and M?
(i) \(P(3,2)\), \(R(3,0)\), \(Q(3,-1)\)
(ii) 0
In which quadrant or on which axis each of the following points lie?
\((-3,5)\), \((4,-1)\), \((2,0)\), \((2,2)\), \((-3,-6)\)
II, IV, x-axis, I, III
Which of the following points lie on y-axis?
A \((1,1)\), B \((1,0)\), C \((0,1)\), D \((0,0)\), E \((0,-1)\), F \((-1,0)\), G \((0,5)\), H \((-7,0)\), I \((3,3)\)
C, D, E, G
Plot the points \((x,y)\) given by the following table. Use scale 1 cm = 0.25 units.
| \(x\) | 1.25 | 0.25 | 1.5 | -1.75 |
|---|---|---|---|---|
| \(y\) | -0.5 | 1 | 1.5 | -0.25 |
A point lies on the x-axis at a distance of 7 units from the y-axis. What are its coordinates?
What will be the coordinates if it lies on y-axis at a distance of -7 units from x-axis?
\((7,0)\), \((0,-7)\)
Find the coordinates of the point:
(i) which lies on x and y axes both.
(ii) whose ordinate is -4 and which lies on y-axis.
(iii) whose abscissa is 5 and which lies on x-axis.
(i) \((0,0)\)
(ii) \((0,-4)\)
(iii) \((5,0)\)
Taking 0.5 cm as 1 unit, plot the following points on the graph paper:
A \((1,3)\), B \((-3,-1)\), C \((1,-4)\), D \((-2,3)\), E \((0,-8)\), F \((1,0)\)
Points \(A(5,3)\), \(B(-2,3)\) and \(D(5,-4)\) are three vertices of a square \(ABCD\). Plot these points on a graph paper and hence find the coordinates of the vertex \(C\).
\(C(-2,-4)\)
Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the third quadrant.
\((0,0)\), \((-5,0)\), \((0,-3)\)
Plot the points \(P(1,0)\), \(Q(4,0)\) and \(S(1,3)\). Find the coordinates of the point \(R\) such that \(PQRS\) is a square.
\(R(4,3)\)
From the Fig. 3.8, answer the following:
(i) Write the points whose abscissa is 0.
(ii) Write the points whose ordinate is 0.
(iii) Write the points whose abscissa is \(-5\).
(i) A, L and O
(ii) G, I and O
(iii) D and H
Plot the points \(A(1,-1)\) and \(B(4,5)\).
(i) Draw a line segment joining these points. Write the coordinates of a point on this line segment between the points A and B.
(ii) Extend this line segment and write the coordinates of a point on this line which lies outside the line segment AB.
(i) \((2,1)\)
(ii) \((5,7)\)