Rs Aggarwal 2021 2022 for Class 9 Maths Chapter 5 - Coordinate Geometry

Answer:

(i)


(ii)


(iii)


(iv)


(v)


(vi)


(vii)


(viii)


(ix)


(x)


(xi)


(xii)

Answer:

Draw perpendicular AL, BM, CN, DP and EQ on the X-axis.




(i) Distance of A from the Y-axis = OL = -6 units
Distance of A from the X-axis = AL = 5 units
Hence, the coordinates of A are (-6,5).

(ii) Distance of B from the Y-axis = OM = 5 units
Distance of B from the X-axis = BM = 4 units
Hence, the coordinates of B are (5,4).

(iii) Distance of C from the Y-axis = ON = -3 units
    Distance of C from the X-axis = CN = 2 units
    Hence, the coordinates of C are (-3,2).

(iv) Distance of D from the Y-axis = OP = 2 units
   Distance of D from the X-axis = DP = -2 units
    Hence, the coordinates of D are (2,-2).

(v) Distance of E from the Y-axis = OL = -1 units
     Distance of E from the X-axis = AL = -4 units
     Hence, the coordinates of E are (-1,-4).

Answer:

(i) (–6, 3)
Points of the type (–, +) lie in the II quadrant.
Hence, the point lies (–6, 3) in the II quadrant.

(ii) (–5, –3)
Points of the type (–, –) lie in the III quadrant.
Hence, the point lies (–5, –3) in the III quadrant.

(iii) (11, 6)
Points of the type (+, +) lie in the I quadrant.
Hence, the point lies (11, 6) in the I quadrant.

(iv) (1, –4)
Points of the type (+, –) lie in the IV quadrant.
Hence, the point lies (1, –4) in the IV quadrant.

(v) (–7, –4)
Points of the type (–, –) lie in the III quadrant.
Hence, the point lies (–7, –4) in the III quadrant.

(vi) (4, –1)
Points of the type (+, –) lie in the IV quadrant.
Hence, the point lies (4, –1) in the IV quadrant.

(vii) (–3, 8)
Points of the type (–, +) lie in the II quadrant.
Hence, the point lies (–3, 8) in the II quadrant.

(viii) (3, –8)
Points of the type (+, –) lie in the IV quadrant.
Hence, the point lies (3, –8) in the IV quadrant.

Answer:

(i) (2, 0)
The ordinate of the point (2, 0) is zero.
Hence, the (2, 0) lies on the x-axis.

(ii) (0, –5)
The abscissa of the point (0, –5) is zero.
Hence, the (0, –5) lies on the y-axis.

(iii) (–4, 0)
The ordinate of the point (–4, 0) is zero.
Hence, the (–4, 0) lies on the x-axis.

(iv) (0, –1)
The abscissa of the point (0, –1) is zero.
Hence, the (0, –1) lies on the y-axis.

Answer:

(i) A(0, 8)
The given point does not lies on the x-axis.

(ii) B(4, 0)
The ordinate of the point (4, 0) is zero.
Hence, the (4, 0) lies on the x-axis.

(iii) C(0, –3)
The given point does not lies on the x-axis.

(iv) D(–6, 0)
The ordinate of the point (–6, 0) is zero.
Hence, the (–6, 0) lies on the x-axis.

(v) E(2, 1)
The given point does not lies on the x-axis.

(vi) F(–2, –1)
The given point does not lies on the x-axis.

(vii) G(–1, 0)
The ordinate of the point (–1, 0) is zero.
Hence, the (–1, 0) lies on the x-axis.

(viii) H(0, –2)
The given point does not lies on the x-axis.

Answer:

Abscissa of D = Abscissa of A = 2
Ordinate of D = Ordinate of B = 2

Now,
BC = (2 + 4) units = 6 units
AD = (5 – 2) units = 3 units

$$\begin{gathered} \mathrm{Area} \mathrm{of} ∆ABC=\frac{1}{2}\times \mathrm{Base}\times \mathrm{Height} \\ =\frac{{\displaystyle 1}}{{\displaystyle 2}}\times BC\times AD \\ =\frac{1}{2}\times 6\times 3 \\ =9 \end{gathered}$$

Hence, area of ∆ABC is 9 square units.

Answer:

Let A(3, 1), B(–3, 1) and C(–3, 3) be three vertices of a rectangle ABCD.

Let the y-axis cut the rectangle ABCD at the points P and Q respectively.



Abscissa of D = Abscissa of A = 3.
Ordinate of D = Ordinate of C = 3.

∴ coordinates of D are (3, 3).

AB = (BP + PA) = (3 + 3) units = 6 units.
BC = (OQ – OP) = (3 – 1) units = 2 units.

Ar(rectangle ABCD) = (AB × BC)
                                  = (6 × 2) sq. units
                                  = 12 sq. units

Hence, the area of rectangle ABCD is 12 square units.

Answer:

Points of the type (–, –) lie in the III quadrant.
The point (–7, –4) lies in the III quadrant.

Hence, the correct option is (c).

Answer:

Answer:

Ans (b)

Explanation:
Points of the type (-,+) lie in the second quadrant.
Hence, the point P(a,b), where a < 0 and b > 0, lie in quadrant II.

Answer:

Answer:

(c) I or III

​Explanation:
If abscissa = ordinate, there could be two possibilities.
Either both are positive or both are negative. So, a point could be either (+,+), which lie in quadrant I or it could be of the type (-,-), which lie in quadrant III.
Hence, the points (other then the origin) for which the abscissas are equal to the ordinates lie in quadrant I or III.

Answer:

The point (–5, 3) lies in the II quadrant.
The point (3, –5) lies in the IV quadrant.

Hence, the correct option is (c).

Answer:

The point (1, –1) lies in the IV quadrant.
The point (2, –2) lies in the IV quadrant.
The point (–3, –4) lies in the III quadrant.
The point (4, –5) lies in the IV quadrant.

Hence, the correct option is (d).

Answer:

The abscissa of the point (0, –8) is zero.
The point (0, –8) lies on the y-axis.

Hence, the correct option is (d).

Answer:

The point (–7, 0) lies on the negative direction of the x-axis.

Hence, the correct option is (a).
 

Answer:

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).

Hence, the correct option is (b).

Answer:

The ordinate of every point on the x-axis is 0.

Hence, the correct option is (c).

Answer:

The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on the y-axis is of the form (0, y).

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

Hence, the correct answer is option (b).

Answer:

The point O(0, 0) is the origin.

A(3, 0) lies on the positive direction of x-axis.

B(3, 4) lies in the Ist quadrant.

C(0, 4) lies on the positive direction of y-axis.

The points O(0, 0), A(3, 0), B(3, 4) and C(0, 4) can be plotted on the Cartesian plane as follows:



Here, the figure OABC is a rectangle.

Hence, the correct answer is option (b).

Answer:

The given points are A(–2, 3) and B(–3, 5).

Abscissa of A = x-coordinate of A = –2

Abscissa of B = x-coordinate of B = –3

∴ Abscissa of A – Abscissa of B = –2 – (–3) = –2 + 3 = 1

Hence, the correct answer is option (b).

Answer:

The perpendicular distance of a point from the y-axis is equal to the x-coordinate of the point.

∴ Perpendicular distance of the point A(3, 4) from the y-axis = x-coordinate of A(3, 4) = 3



Hence, the correct answer is option (a).

Answer:

(b) I and IV quadrants

​Explanation:
If abscissa of a point is positive, then the ordinate could be either positive or negative.
It means that the type of any point can be either (+,+) or (+, -). 
Points of the type (+,+) lie in quadrant I, whereas points of the type (+,-) lie in quadrant IV.

Answer:

(c) the origin
​Explanation: The point at which two axes meet is called as the origin.

Answer:

The ordinate of a point is the y-coordinate of the point. So, the y-coordinate of the point is 3.

Also, any point on the y-axis has coordinates in the form (0, y).

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

Hence, the correct answer is option (b).

Answer:

(b) (3,9)

Explanation:
Point (2,8) does not satisfy the equation y = 2x + 3.              (​∵ y = 2 × 2 + 8 = 12$\ne$ 8)
Point (3,9) satisfy the equation y = 2x + 3.                             (​∵ y =2 × 3 + 3 = 9)
Point (4,12) does not satisfy the equation y = 2x + 3.    (∵ y = 2 × 4 + 3 = 11$\ne$ 12)
Point (5,15) does not satisfy the equation y = 2x +3.    (∵ y= 2 × 5 + 3 = 13$\ne$15)
Hence, the point (3,9) lies on the line ​y = 2x +3. 

Answer:

(d) (4,12)

Explanation:
(a) Point (1,7) satisfy the equation y = 3x + 4.                      (∵y = 3 × 1 + 4 = 7)
(b) Point (2,10) satisfy the equation y = 3x + 4.                    (∵y = 3 × 2 + 4 = 10)
(c) Point (-1,1) satisfy the equation y = 3x + 4.                     (∵y = 3 × -1 + 4 = 1)
(d) Point (4,12) does not satisfy the equation y = 3x + 4.    (∵ y = 3 × 4 + 4 = 16 ≠ 12)
Hence, the point (4,12) do not lie on the line y = 3x +4.

Answer:

The point (3, –6) lies in the fourth quadrant.

The point (–3, 4) lies in the second quadrant.

The point (5, 7) lies in the first quadrant.

The point (0, 3) lies on the positive direction of y-axis.



Thus, the point (0, 3) does not lie in any quadrant.

Hence, the correct answer is option (d).

Answer:

The points A(0, 6), O(0, 0) and B(6, 0) can be plotted on the Cartesian plane as follows:



Here, ∆AOB is a right triangle right angled at O.

OA = 6 units and OB = 6 units

∴ Area of ∆AOB = $\frac{1}{2}\times \mathrm{OA}\times \mathrm{OB}=\frac{1}{2}\times 6\times 6$ = 18 square units

Hence, the correct answer is option (c).