Class 9 R S AGGARWAL AND V AGGARWAL Solutions Maths Chapter 5: Coordinate Geometry
Coordinate Geometry Exercise 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.
Coordinate Geometry Exercise 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