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Q1. The coordinates of the origin 

• 1) (-x, -y)
• 2) (0, 0)
• 3) (x, y)
• 4) None of these

Solution

The coordinates of the origin is (0, 0). 

Q2. Two points having the same abscissae but different ordinates lie on 

• 1) the x-axis
• 2) a line parallel to the y-axis
• 3) the y-axis
• 4) a line parallel to the x-axis

Solution

According to the question, two points have the same x coordinate but different y coordinate. These points are (x, a), (x, b), ….  Hence, a line is parallel to the y-axis 

Q3. A point lies on x-axis at a distance of 9 units from y-axis. What are its coordinates? What will be its coordinates if it lies on y axis at a distance of -9 units from x-axis?

Solution

Since the point lies on x-axis at a distance of 9 units from y-axis. Its coordinates will be (9, 0). If it lies on y axis at a distance of -9 units from x-axis, its coordinates will be (0, -9)

Q4. Plot the points A (3,0), B (3,3) and C (0,3) in a Cartesian plane. Join OA, AB, BC and CO, where O represents the origin. Name the figure so formed and write its one property.

Solution

The figure obtained is a square OABC with each side 3 units. Where: O(0,0),A(3,0),B(3,3,) And C(0,3). All sides of the square are equal ,i.e. OA=AB=BC=OC.

Q5. What are the coordinates of the foot of the perpendicular drawn from (4, 3) on the y-axis? 

• 1) (-3, 0)
• 2) (0, 3)
• 3) (4, 3)
• 4) (0, 4)

Solution

(0, 3) is the coordinate of the foot of the perpendicular drawn from (4, 3) on the y-axis. 

Q6. Plot the points (3,2), (-2,2), (-2,-2) and (3,-2) in the Cartesian plane. Join these points and name the figure so formed.

Solution

ABCD is a rectangle.

Q7. Plot the point P(2,-6) on graph paper and from it draw PM and PN as perpendicular to x - axis and y - axis, respectively. Write the coordinates of the points M and N.

Solution

From P(2,-6) we draw perpendiculars PM to x-axis and perpendicular PN to y-axis then, Coordinates of :- N(0,-6) and M (2,0)

Q8. The point whose abscissa is -3 and lies on x-axis is.

• 1) (0,3)
• 2) (-3,0)
• 3) (0,-3)
• 4) (3,0)

Solution

Given x = -3 and point on x-axis is of the form (x,0).So, (-3,0) is the required point.

Q9. Two points having different abscissae but the same ordinates lie on

• 1) the x-axis
• 2) a line parallel to the x-axis
• 3) the y-axis
• 4) a line parallel to the y-axis

Solution

According to the question, two points have different x coordinates but the same y coordinate. These points are (a, y), (b, y), ….  Hence, a line is parallel to the x-axis.

Q10. In figure, AOB is a triangle with coordinates of A and O as (4,0) and (0,0). If AB = 5, find the coordinates of B.

Solution

5² = 4² + OB² OB² = 25 - 16 = 9 Thus, OB = 3 B is on +ve side of y-axis Co- ordinates of B are (0, 3).

Q11. If the abscissa of a point is y and the ordinate is x, then the coordinates of the point are 

• 1) (0, y)
• 2) (x, 0)
• 3) (y, x)
• 4) (x, y)

Solution

According to the question, the x coordinate is y and the y coordinate is x. Hence, the coordinates of the point are (y, x). 

Q12.  Point (-3,-5) lies in the ______ quadrant.

• 1) Fourth quadrant
• 2) Third quadrant
• 3) Second quadrant
• 4) First quadrant

Solution

The given point lies in third quadrant since both the coordinates are negative.

Q13. Point (0,4) lies:

• 1) On x axis
• 2) In I quadrant
• 3) On y axis
• 4) In IV quadrant

Solution

On y axis

Q14. What is the ordinate of a point (-3, -9)? 

• 1) -9
• 2) -3
• 3) 9
• 4) 3

Solution

The y coordinate is called an ordinate. 

Q15. Plot the points O(0,0), B(16,0), C(16,12) on the graph paper. Join points O, B and C. Name the figure.

Solution

Here OBC forms a right angled triangle

Q16. Draw a quadrilateral whose vertices are (3,2), (2,3), (-4,5) and (5,-3).

Solution

Q17. Where would the point (x, y) lie if x ≠ y ≠ 0 and either x > 0 and y < 0 or x < 0 and y > 0? 

• 1) 3^rd and 4^thquadrants
• 2) 1^st and 2^ndquadrants
• 3) 1^st and 3^rdquadrants
• 4) 2^nd and 4^thquadrants

Solution

x < 0, y > 0 which is (-, +); hence, it would lie in the 2^nd quadrant. x > 0 , y > 0 which is (+, -); hence, it would be lie in the 4^th quadrant.

Q18. Ram, Shyam and Anil are three friends standing at three different positions. Ram and Anil are in opposite direction but are at equal distance from Shyam. Shyam is at origin and position of Ram is (0,8). If the abscissa of position of Anil is 0, then what are the coordinates of Anil's position?

Solution

Q19. The perpendicular distance of the point (-5, 4) from the x-axis is 

• 1) 4
• 2) 5
• 3) -5
• 4) -4

Solution

The perpendicular distance of the point (-5, 4) from the x-axis is always the y coordinate. Hence, it is 4 units. 

Q20. In which quadrant do the given points lie? (a) (2, -1) (b) (-1, 7) (c) (-2, -3) (d) (4, 5)

Solution

(a) 4^th quadrant (b) 2^nd quadrant (c) 3^rd quadrant (d) 1^st quadrant

Q21. In figure, ABCD is a square. Find the co-ordinates of point A and D.

Solution

A = (-1,3) D = (2,-2)

Q22. The following table gives the number of pairs of shoes and their corresponding price. Plot these as ordered pairs and join them. What type of graph do you get? Number of pairs of shoes 1 2 3 4 5 6 Corresponding prices (in hundred or rupees) 5 10 15 20 25 30

Solution

The graph obtained is a straight line.

Q23. In which quadrant does the point (-1, 3) lie?

• 1) II
• 2) I
• 3) III
• 4) IV

Solution

Point (-1, 3) lies in II quadrant.

Q24. Which of the following is correct? 

• 1) While plotting a point in a plane, the y coordinate always comes first.
• 2) While plotting a point in a plane, the x coordinate always comes second.
• 3) If the x coordinate is a and the y coordinate is b, then point is (b, a).
• 4) None of these

Solution

A, B and C are incorrect. 

Q25. The origin lies on the 

• 1) only on y-axis
• 2) Both axes
• 3) only on x-axis
• 4) 1^st quadrant

Solution

The origin is the intersection of both axes. Hence, it lies on both axes. 

Q26. If the coordinates of two points are A (-2, 5) and B (4, -6), then (abscissa of A) - (abscissa of B) is 

• 1) -8
• 2) 1
• 3) 2
• 4) 4

Solution

Abscissa of A is -2 and abscissa of B is -6. (abscissa of A) - (abscissa of B) = -2 - (-6) = -2 + 6 = 4 

Q27. In the figure, is an equilateral triangle with coordinates of vertices B and C as (-4, 0) and (4, 0) respectively. Find the coordinates of the point A

Solution

Q28. Mark the points (2,2), (2, -2), (-2,-2) and (-2,2) on a graph paper and join these points. Name the figure that you obtain. Also, find the area of the figure so obtained.

Solution

The figure obtained is a square. Area of square =side x side = 4 4=16 sq. units 

Q29. A point (x, y) lies in the 

• 1) 2^nd and 3rd quadrants
• 2) 2^nd and 4^thquadrants
• 3) 1st and 2nd quadrants
• 4) 1^st and 3rd quadrants

Solution

If  then either x or y is negative. Hence, the point lies in the second and fourth quadrants. 

Q30. In the given (i)       Write the x-coordinates and the y-coordinates of the  points P , Q, R. (ii)      The coordinates of point S (iii)      Find the abscissa of the point T (iv)      Find the point whose coordinates are ( 5, 3) (v)       Find the ordinates of points P and R.

Solution

(i)  P ( 6, 3)   ;    Q ( -3, 2)  ; R( -4, -7)  (ii) S (4,-6) (iii)  6 (iv)   V (v)    3 and -7

Q31. Find the area of the triangle formed by (0,4),(0,0),(3,0).

Solution

Q32. Observe figure, and answer the following: (A) co-ordinate of B. (B) Point identified by the co-ordinates (-2, -3). (C) Abscissa of point D. (D) Ordinate of point H. (E) Points with same abscissa. (F) Points with same ordinate.

Solution

(A) (2,3) (B) A (C) 0 (D) 0 (E) B,G (E) M,H

Q33. The point from which distances are marked is called 

• 1) x-axis
• 2) Coordinate
• 3) y-axis
• 4) Origin

Solution

The point from which distances are marked is called the origin. 

Q34. In figure, ABC is an equilateral triangle with co-ordinate of B and C as (1,0), (5,0). Find the co-ordinate of vertex A.

Solution

In equilateral triangle ABC, BC = 4 unit, AC = 4 unit, AB = 4 unit Drop a perpendicular from A to x-axis. AP² = AB² - BP² = (4)² - (2)² = 16 - 4 = 12 AP = So co-ordinates of A are

Q35. The following table gives the number of pens and their corresponding costs. Plot these as ordered pairs and join them. What type of graph do you get? Number of Pens 1 2 4 5 7 8 Price in rupees 3 6 12 15 21 24

Solution

The graph is a straight line.

Q36. The perpendicular distance of a point from the x - axis is 4 units and the perpendicular distance from the y - axis is 5 units. Write the coordinates of such a point if it lies in the (i) I Quadrant (ii) II Quadrant (iiii) III Quadrant (iv) IV Quadrant

Solution

(i) In the first quadrant, the coordinates of the required point will be (5,4). (ii) In the second quadrant, the coordinates of the required point will be (-5,4). (iii) In the third quadrant, the coordinates of the required point will be (-5,-4). (iv) In the fourth quadrant, the coordinates of the required point will be (5,-4).

Q37. Plot the points (2,3) (-2,3) (-2,-3) and (2,-3) on a graph sheet. Join these points. Name the figure obtained. Also, find the area of the figure so obtained.

Solution

Rectangle of length 6 units Breadth 4 cm Area = 4 6 = 24 (units)²

Q38. Which of the following points lie on x-axis? Which on y-axis? A(0,2), B(5,6), C(-3,0), D(0,-3), E(0,4), F(6,0), G(3,0)

Solution

If x-coordinate of a point is zero then it lies on y-axis and if y-coordinate is zero then it lies on x-axis. Points on x-axis : C(-3,0), F(6,0), G(3,0) Points on y-axis : A(0,2), D(0,-3), E(0,4)

Q39. In figure,  and  are equilateral triangle. Find coordinates of point C and D.

Solution

Coordinates of point C are (0, a). Coordinates of point D are (0, -a).

Q40. The point (4, -6) lies in the 

• 1) 1^st quadrant
• 2) 4^th quadrant
• 3) 3^rd quadrant
• 4) 2^nd quadrant

Solution

In the 3rd quadrant, the x coordinate is positive and the y coordinate is negative. 

Q41. A car starts from the center of city and in each consecutive hour it covers a distance of 20km (along north), 16 km (along east), 24 km (along south) and 20 km (along west) respectively. Assuming the centre of city to be the origin, north-south direction is along y axis and west-east direction is along x axis; show the various position of the car on the Cartesian plane. Also, find how far is the car from x and y axis respectively at its final position.

Solution

Q42. Which of the following represents a line parallel to x-axis?

• 1) x + y = 7
• 2) y + 2 = 2y - 5
• 3) 5x + 3 = 4
• 4) x + 3 = 0

Solution

y + 2 = 2y - 5 2y - y = 2 + 5 y = 7 Since for all the values of x, value of y = 7, therefore, the line will be parallel to x-axis.

Q43. What would be the coordinates of the foot of perpendicular drawn from (3,2) on y-axis?

Solution

Q44. Which of the following point lies in the first quadrant? 

• 1) (-x, y)
• 2) (-x, -y)
• 3) (x, y)
• 4) (x, -y)

Solution

In the first quadrant, both coordinates are positive. 

Q45. Which of the following points do not lie on the line 3y = 6 - 2x.(i) (3,0)(ii) (2,2)(iii) (0,2)

Solution

Q46. In fig., ABCD is a rectangle with length 6 cm and breadth 3 cm. O is the mid-point of AB. Find the coordinates of A, B, C and D.

Solution

ABCD is a rectangle where AB = CD= 6cm AD = BC = 3cm As O is the midpoint of AB, OA=OB=3cm So, co-ordinates of A will be O(0,0)+3 units in x'-axis = (-3,0) Co-ordinates of A (-3,0) Similarly co-ordinates of B (3,0) Again, BC=3 So, co-ordinates of C will be B(3,0)+3 units in y-axis = (3,3) Similarly co-ordinates of D (-3,3)

Q47.

Solution

Q48. Using the graph given below, find the following : (i) Abssica of P (ii) Ordinate of Q(iii) Coordinate of V(iv) Point on X axis(v) Point of  Y axis (vi) Point in I quadrant(vii) Point in II quadrant(viii) Point in III quadrant(ix) Point in IV quadrant  

Solution

(i) Abscissa of P is 2(ii) Ordinate of Q is - 5(iii) V (-2,2)(iv) S (4,0)(v) T (0,4)(vi) P (2,3)(vii) U (-4,3)(viii) V (-2,2)(ix) Q (3,-5)

Q49. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular distance from the y-axis is 3 units. Write the co-ordinates of the point if it lies in the: (i) I Quadrant (ii) II Quadrant (iii) III Quadrant (iv) IV Quadrant

Solution

x co-ordinate 3, y co-ordinate 2

Q50. What would be the reflection of (1,2) in IV quadrant?

Solution

Q51. Locate the following points in the Cartesian plane: A(3,0), B(0,5), C(-3,-5) and D(2,4).

Solution