R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 5 - Coordinate Geometry

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Chapter 5 - Coordinate Geometry MCQ

Solution 1

Correct option: (c)

Since, both the coordinates of given point are negative, it lies in Quadrant III. 

Solution 2

Correct option: (d)

  

Solution 3

Correct option: (b)

Since, x co-ordinate is negative and y co-ordinate is positive, the given point lies in Quadrant II.

Solution 4

Correct option: (c)

  

  

Solution 5

Correct option: (c)

  

  

Solution 6

Correct option: (c)

For point (-5, 3), the x co-ordinate is negative and the y co-ordinate is positive. Hence, it lies in Quadrant II.

For point (3, -5), the x co-ordinate is positive and the y co-ordinate is negative. Hence, it lies in Quadrant IV.

Solution 7

Correct option: (d)

Points (1, -1), (2, -2) and (4, -5) lie in Quadrant IV, but point (-3, -4) lies in Quadrant III.

Hence, all the given points do not lie in the same quadrant. 

Solution 8

Correct option: (d)

Point (0, -8) lies on y-axis as its x co-ordinate is 0. 

Solution 9

Correct option: (a)

Point (-7, 0) lies on negative direction of the x-axis as its x co-ordinate is negative and y co-ordinate is zero. 

Solution 10

Correct option: (b)

The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is (0, -5). 

Solution 11

Correct option: (c)

The ordinate (y co-ordinate) of every point on the x-axis is 0. 

Solution 12

Correct option: (b)

If the y-coordinate of a point is zero then this point always lies on the x-axis. 

Solution 13

Correct option: (b)

By plotting the given points, we find that figure OABC is a rectangle.

  

Solution 14

Correct option: (b)

Abscissa of A - Abscissa of B

= -2 - (-3)

= -2 + 3

= 1 

Solution 15

Correct option: (a)

The perpendicular distance of the point A(3, 4) from the y-axis is 3 units. 

Solution 16

Correct option: (b)

  

  

Solution 17

  

Solution 18

Correct option: (b)

If a point lies on y-axis, then its abscissa is 0.

Hence, the point whose ordinate is 3 and which lies on the y-axis is (0, 3). 

Solution 19

  

Solution 20

  

Solution 21

Correct option: (d)

The abscissa of point (0, 3) is 0. Hence, it lies on y-axis. 

Solution 22

Correct option: (c)

  

Clearly, ΔAOB is a right-angled triangle.

Chapter 5 - Coordinate Geometry Ex. 5

Solution 1

The given points are plotted as follows:

  

Solution 2

Draw the perpendiculars from the AF, BG, CH, DI and EJ on the x-axis.

(1) The distance of A from the y-axis = OF = -6 units

     The distance of A from the x-axis = AF = 5 units

     Hence, the coordinate of A are (-6, 5)

(2)The distance of B from the y-axis = OG = 5 units

     The distance of B from the x-axis = BG = 4 units

     Hence, the coordinate of B are (5, 4)

(3)The distance of C from the y-axis = OH = -3 units

     The distance of C from the x-axis = HC = 2 units

     Hence, the coordinate of C are (-3, 2)

(4)The distance of D from the y-axis = OI = 2 units

     The distance of D from the x-axis = ID = -2 units

     Hence, the coordinate of D are (2, -2)

(5)The distance of E from the y-axis = OJ = -1 unit

     The distance of E from the x-axis = JE = -4 units

     Hence, the coordinate of E are (-1, -4)

Thus, the coordinates of A, B, C, D and E are respectively, A(-6,5), B(5,4), C(-3,2), D(2,-2) and E(-1,-4)

Solution 3

(i) (-6, 3):

 x co-ordinate is negative and y co-ordinate is positive.

 Hence, (-6, 3) lies in the 2nd Quadrant.

 

(ii) (-5, -3) :

 x co-ordinate and y co-ordinate both are negative.

 Hence, (-5, -3) lies in the 3rd Quadrant.

 

(iii) (11, 6):

  x co-ordinate and y co-ordinate both are positive.

  Hence, (11, 6) lies in the 1st Quadrant.

 

(iv) (1, -4):

 x co-ordinate is positive and y co-ordinate is negative.

  Hence, (1, -4) lies in the 4th Quadrant.

 

(v) (-7, -4):

 x co-ordinate and y co-ordinate both are negative.

 Hence, (-7, -4) lies in the 3rd Quadrant.

 

(vi) (4, -1):

 x co-ordinate is positive and y co-ordinate is negative.

 Hence, (4, -1) lies in the 4th Quadrant.

 

(vii) (-3, 8):

 x co-ordinate is negative and y co-ordinate is positive.

 Hence, (-3, 8) lies in the 2nd Quadrant.

 

(viii) (3, -8):

 x co-ordinate is positive and y co-ordinate is negative.

 Hence, (3, -8) lies in the 4th Quadrant. 

Solution 4

(i) (2, 0) lies on the x-axis as the co-ordinates of every point on the x-axis are of the form (x, 0).

(ii) (0, -5) lies on the y-axis as the co-ordinates of every point on the y-axis are of the form (0, y).

(iii) (-4, 0) lies on the x-axis as the co-ordinates of every point on the x-axis are of the form (x, 0).

(iv) (0, -1) lies on the y-axis as the co-ordinates of every point on the y-axis are of the form (0, y). 

Solution 5

The co-ordinates of every point on the X-axis are of the form (x, 0).

Hence, following points lie on the x-axis:

(ii) B(4, 0)  

(iv) D(-6, 0)

(vii) G(-1, 0) 

Solution 6

The given points are plotted on the graph paper as follows:

Solution 7

The given vertices of rectangle ABCD are plotted on graph paper as follows:

The coordinates of fourth vertex D are (3, 3)

Area of rectangle ABCD = Length × Breadth

= AB × BC

= 6 × 2 

= 12 square units