Question 1. A point (other than zero) is such that [The abscissa of the point] = [The ordinate of the point] In which quadrants can the point lie?
Solution: ∵ The coordinates have opposite signs in II and IV quadrants.
∴ the given point lies in I or III quadrant.
Question 2. A line ∠M is drawn parallel to X-axis at a distance of 5 units from it. On ∠M a point P is marked at a distances of 3 units from the Y-axis. What are the coordinates of P?
Solution: The line ∠M can be above or below the x-axis
∴ co-ordiantes of P are (3, 5) or (–3, 5)
Question 3. Which of the following statements are true?
(i) The point (0, –4) lies on y-axis
(ii) The perpendicular distance of the point (5, 7) from the x-axis is 5.
(iii) Point (1, –1) and (–1, 1) lie in the same quadrant.
Solution: Only the statement (i) is true.
Question 4. What are the coordinates of origin?
Solution: (0, 0) are the coordinates of origin.
Question 5. What is the sign of y-coordinate below the x-axis?
Solution: It is always negative.
Question 6. What is the x-coordinate of a point on y-axis?
Solution: It is always ‘0’.
Question 7. In which quadrant the point (–2, 5) lies?
Solution: (–2, 5) lies in the II-quadrant.
Question 8. What is the sign of the y-coordinate of a point lying in the III-quadrant?
Solution: The y-coordinate of a point in III-quadrant is always negative.
Question 9. If the two points are A(–2, 7) and B(–3, 4) then what is (abscissa of A) – (abscissa of B)?
Solution: ∵ abscissa of A = – 2 and abscissa of B = – 3
∵ (– 2) – (– 3) = –2 + 3 =1
Question 10. If the y-coordinate of a point is zero, then where does this point lie?
Solution: It lies on the x-axis.
Question 11. What are the coordinates of a point lying on the y-axis at negative 3 units?
Solution: (0, –3)
Question 12. What are the coordinates of a point whose ordinate is 5 and lying on the y-axis.
Solution: (0, 5).
Question 13. In the following figure, which point has its abscissa as –3
Solution: The point p(–3, 3) has its abscissa as –3.
Question 14. Name the collinear points in the above figure?
Solution: The points P, O and R are collinear.
Question 15. What is the distance of the point (3, – 4) from x-axis?
Solution: –4 units.
Question 16. The origin lies on which of the following? x-axis only, both axis, none of the axes
Solution: The origin lies on both the axes.
Question 17. The abscissa of a point is 5 and it lies on the x-axis. What are its coordinates?
Solution: (5, 0).
Question 18. A point lies on the x-axis as well as on the y-axis. What are its coordinates?
Solution: (0, 0)
Question 19. In which quadrants x and y coordinates have different sign
Solution: II and IV quadrants.
Question 20. In which quadrants x and y coordinate have same sign?
Solution: I and III quadrants.