Consider the three statements given below:
I. Any point on x-axis is of the form (a, 0).
II. Any point on y-axis is of the form (0, b).
III. The point P(3, 3) lies on both the axes.
Which is true?
(a) I and II
(b) I and III
(c) II and III
(d) III only

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Solution

(a) I and II

Explanation:
Ordinates of points lying on the x-axis = 0
Abscissae of points lying on the y-axis = 0
In point P(3,3), neither the abscissa nor the ordinate is 0. Hence, statements I and II are true.

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Similar questions

Q. Read the statements given below and choose the correct answer:
I. Any point on x-axis is of the form (x, 0) for all x.
II. Any point on y-axis is of the form (0, y) for all y.
III. Any point on both the axes is of the form (x, y) for all x and y.
Which of the following is true?
(a) I and II
(b) I and III
(c) I only
(d) III only

Q. Question 3
Point ( 0, -7) lies

Thinking process
(i) Firstly, check whether any coordinate of the given point is zero or not.
(a) If x-coordinate is zero and y-coordinate is non-zero, then the point lies on the y-axis.
(b) If y-coordinate is zero and x-coordinate is non-zero, then the point lies on the x-axis.
(c) If x-coordinate and y-coordinate are zero, the point lies on the origin ( or on both the axes.)
(ii) If none of the coordinates is zero, then the point lies in any one of the four quadrants.

A) On the x-axis
B) In the second quadrant
C) On the y-axis
D) In the fourth quadrant

Q. Fill in the blanks to make the given statements true.
(i) A point in which the x-coordinate is 0 and y-coordinate is 5 will lie on ..... .
(ii) All point with y-coordinate as 0 lie on ...... .
(iii) The x-coordinate of any point lying on the y-axis is always ..... .
(iv) The point where the two axes intersect is called the ..... .
(v) For the point (5, 2), the distance from the x-axis is ...... units.
(vi) The distance of any point from the y-axis is the ...... coordinate.
(vii) The coordinates of the origin are ...... .

Q. Match the following columns:

Column I	Column II
(a) Equation of x-axis is	(p) (a, 0)
(b) Equation of y-axis is	(q) y = 0
(c) Any point on x-axis is of the form	(r) (0, b)
(d) Any point on y-axis is of the form	(s) x = 0

(a) ......,
(b) ......,
(c) ......,
(d) ......,

Q. For each of the following write true or false
(i) The point (4, 0) lies in quadrant I.
(ii) The ordinate of a point P is −3 and its abscissa is −4. The point is P(−3, −4).
(iii) The points A(1, −1) and B(−1, 1) both lies in quadrant IV.
(iv) A point lies on y-axis at a distance of 3 units from x-axis. Its coordinates are (3, 0).
(v) The point C(0, −5) lies on y-axis.
(vi) The point O(0, 0) lies on x-axis as well as y-axis.

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Consider the three statements given below: I. Any point on x-axis is of the form (a, 0). II. Any point on y-axis is of the form (0, b). III. The point P(3, 3) lies on both the axes. Which is true? (a) I and II (b) I and III (c) II and III (d) III only

(a) I and II Explanation: Ordinates of points lying on the x-axis = 0 Abscissae of points lying on the y-axis = 0 In point P(3,3), neither the abscissa nor the ordinate is 0. Hence, statements I and II are true.

Consider the three statements given below:
I. Any point on x-axis is of the form (a, 0).
II. Any point on y-axis is of the form (0, b).
III. The point P(3, 3) lies on both the axes.
Which is true?
(a) I and II
(b) I and III
(c) II and III
(d) III only

(a) I and II

Explanation:
Ordinates of points lying on the x-axis = 0
Abscissae of points lying on the y-axis = 0
In point P(3,3), neither the abscissa nor the ordinate is 0. Hence, statements I and II are true.