Selina Concise Class 9 Maths Chapter 26 Co-ordinate Geometry Exercise 26B Solutions
EXERCISE – 26B
(Q1) Draw the graph for each linear equation given below.
(i) x = 3
Solution:
X | 3 | 3 | 3 |
y | 4 | 0 | -3 |
x = 3 is parallel to y-axis.
(ii) x + 3 = 0
Solution:
x + 3 = 0
x = -3
X | -3 | -3 | -3 |
y | 0 | 4 | -4 |
(iii) x – 5 = 0
Solution:
x – 5 = 0
x = 5
X | 5 | 5 | 5 |
y |
(iv) 2x – 7 = 0
Solution:
2x – 7 = 0
2x = 7
x = 7/2
x = 3.5
X | 3.5 | 3.5 | 3.5 |
y | 0 | 4 | -4 |
(v) y = 4
Solution:
X | 0 | -4 | 5 |
y | 4 | 4 | 4 |
y = 4 is parallel to x-axis.
(vi) y + 6 = 0
Solution:
y + 6 = 0
y = -6
X | 0 | -5 | 4 |
y | -6 | -6 | -6 |
y = -6 is parallel to x-axis.
(vii) y – 2 = 0
Solution:
y – 2 = 0
y = 2
X | 0 | -3 | 4 |
y | 2 | 2 | 2 |
(viii) 3x + 5 = 0
Solution:
3x + 5 = 0
3x = -5
x = -5/3
x = – 1.6
X | -1.6 | -1.6 | -1.6 |
y | 0 | 3 | -4 |
(ix) 2y – 5 = 0
Solution:
2y – 5 = 0
2y =
y = 5/2
y = 2.5
X | 0 | -4 | 4 |
y | 2.5 | 2.5 | 2.5 |
(x) y = 0
Solution:
X | 0 | -2 | 3 |
y | 0 | 0 | 0 |
(xi) x = 0
Solution:
X | 0 | 0 | 0 |
y | 0 | 3 | -3 |
(Q2) Draw the graph for each linear equation given below:
(i) y = 3x
Solution:
y = 3x
Put x = 0
y = 3 × 0
y = 0
∴ (x, y) = (0, 0)
Put x = 1
y = 3 (1)
y = 3
Put x = -2
y = 3 (-2)
y = -6
X | 0 | 1 | -2 |
y | 0 | 3 | -6 |
(ii) y = -x
Solution:
y = -x
Put = -1
y = -1
Put x = 2
y = -2
Put x = -3
y = +3
X | 1 | 2 | -3 |
y | -1 | -2 | 3 |
(iii) y = – 2x
Solution:
y = -2x
Put x = 1
y = (-2) × 1
y = -2
Put x = -1
y = (-2) × (-1)
y = 2
Put x = 3
y = (-2) × 3
y = -6
X | 1 | -1 | 3 |
y | -2 | 2 | -6 |
(iv) y = x
Solution:
X | 1 | -2 | 4 |
y | 1 | -2 | 4 |
(v) 5x + y = 0
Solution:
5x + y = 0
y = – 5x
Put x = 1
y = (-5) × 1
y = -5
Put x = -2
y = -5 (-2)
y = 10
Put x = 0
y = 0
X | 1 | -2 | 0 |
y | -5 | 10 | 0 |
(vi) x + 2y = 0
Solution:
x + 2y = 0
x = -2y
Put y = 0
x = 0
Put y = 1
x = -2
Put y = 3
x = (-2) × 3
x = -6
X | 0 | -2 | -6 |
y | 0 | 1 | 3 |
(vii) 4x – y = 0
Solution:
4x – y = 0
4x = y
y = 4x
Put x = 0
Put x = 1
y = 4 ×1
y = 4
Put x = -2
y = 4 ×(-2)
y = -8
X | 0 | 1 | -2 |
y | 4 | 4 | -8 |
(viii) 3x + 2y = 0
Solution:
3x + 2y = 0
3x = -2y
x = -2y/3
Put y = 0
x = 0
Put y = 3
x = -2/3 × 3
x = -2
Put y = 6
x = -2/3 × 6
x = -2 ×2
x = -4
X | 0 | -2 | -4 |
y | 0 | 3 | 6 |
(ix) x = -2y
Solution:
x = -2y
Put y = 1
x = 0
Put y = -2
x = (-2) × (-2)
x = 4
X | -2 | 0 | 4 |
y | 1 | 0 | -2 |
(Q3) Draw the graph for each linear equation given below.
(i) y = 2x + 3
Solution:
y = 2x + 3
Put x = 1
y = 2 ×1 + 3
y = 5
Put x = 0
y = 2 (0) + 3)
y = 3
Put x = 2
y = 4 + 3
y = 7
X | 1 | 0 | 2 |
y | 5 | 3 | 7 |
(ii) y = 2x/3 – 1
Solution:
y = 2x/3 – 1
Put x = 0
y = 2/3 (0) – 1
y = -1
Put x = 3
y = 2/3 × 3 – 1
y = 2-1
y = 1
Put x = 6
y = 2/3 × 6 – 1
y = 2 ×2 – 1
y = 4-1
y = 3
X | 0 | 3 | 6 |
y | -1 | 1 | 3 |
(iii) y = -x + 4
Solution:
y = -x + 4
Put x = 0
y = 4
Put x = 1
y = -1 + 4
y = 3
Put x = -2
y = (-2) + 4 = 2+4
y = 6
X | 0 | 1 | -2 |
y | 4 | 3 | 6 |
(iv) y = 4x – 5/2
Solution:
y = 4x – 5/2
Put x = 0
y = -5/2
y = -2.5
Put x = 1
y = 4 – 5/2
y = 8-5/2
= 3/2
y = 1.5
Put x = 2
y = 4 × 2 – 5/2
y = 8-5/2 = 16-5/2
y = 11/2
y = 5.5
X | 0 | 1 | 2 |
y | -2.5 | 1.5 | 5.5 |
(v) y = 3x/2 + 2/3
Solution:
y = 3x/2 + 2/3
Put x = 0
y = 2/3
y = 0.6
Put x = 1
y = 3/2 + 2/3
y = 9+4/6
y = 13/6
y = 2.1
Put x = 2
y = 3/2 × 2 + 2/3
y = 3 + 2/3
y = 9+2/3
y = 11/3
y = 3.6
X | 0 | 1 | 2 |
y | 0.6 | 2.1 | 3.6 |
(vi) 2x – 3y = 4
Solution:
2x – 3y = 4
2x = 4 + 3y
x = 4+3y/2
x = 4/2 + 3/2y
x = 2 + 3/2 y
Put y = 1
x = 2 + 3/2
x = 4 + 3/2
x = 7/2
x = 3.5
Put y = 0
x = 2
Put y = -1
x = 2 + 3/2 (-1)
= 2 – 3/2
x = 4-3/2
x = 1/2
x = 0.5
X | 3.5 | 2 | 0.5 |
y | 1 | 0 | -1 |
(viii) x – 3 = 2/3 (y + 1)
Solution:
x – 3 = 2/3 (y + 1)
3 (x – 3) = 2 (y + 1)
3x – 9 = 2y + 2
3x – 2y = 2+9
3x – 2y = 11
3x = 11+2y
x = 11+2y/3
x = 11/3 + 2/3 y
Put y = 0
x = 11/3
x = 3.6
Put y = 1
x = 11/3 + 2/3
= 11+2/3
x = 13/3
x = 4.3
Put y = -1
x = 11/3 – 2/3
= 11-2/3
= 9/3
x = 3
X | 3.6 | 4.3 | 3 |
y | 0 | 1 | -1 |
(ix) x + 5y + 2 = 0
x + 5y + 2 = 0
x = -5y – 2
Put y = (-1)
x = -5 (-1) – 2
= 5 – 2
x = 3
Put y = 1
x = -5-2
x = -7
X | -2 | 3 | -7 |
y | 0 | -1 | 1 |
(Q4) Draw the graph for each equation given below:
(i) 3x + 2y = 6
(ii) 2x – 5y = 10
(iii) 1/2 x + 2/3 y = 5
(iv) 2x-1/3 – y-2/5 = 0
In each case, find the co-ordinates of the points where the graph (line) drawn meets the co-ordinates axes.
(i) 3x + 2y = 6
Solution:
3x = 6 – 2y
Put y = 0
x = 6-2y/3
x = 2 – 2/3 y
x = 2
Put y = 1
x = 2 – 2/3
x = 6-2/3
x = 4/3
x = 1.3
Put y = -1
x = 2 + 2/3
x = 8/3
x = 2.6
The co-ordinates of the points which meets the co-ordinates axes is –
(0, 3) and (2, 0)
X | 2 | 1.3 | 2.6 | 0 |
y | 0 | 1 | -1 | 3 |
(Q4) (ii) 2x – 5y = 10
Solution:
2x = 10 + 5y
x = 10/2 + 5/2 y
x = 5 + 5/2 y
x – 5 = 5/2 y
2 (x-5)/5 = y
2x – 10/5 = y
2x/5 – 2 = y
Put x = -1
-2/5 – 2 = y
-2-10/5 = y
-12/5 = y
-2.4 = y
Put x = 0
y = -2
Put x = 1
y = 2/5 (1) – 2
y = 2/5 – 2
y = 2 – 10/5
y = -8/5
y = 1.6
X | -1 | 0 | 1 |
y | -2.4 | -2 | -1.6 |
The co-ordinates of the points which meets the co-ordinates axes is (0, -2), and (5, 0)
(iii) 1/2 x + 2/3 y = 5
Solution:
1/2 x + 2/3 y = 5
2/3 y = 5 – 1/2 x
Multiply by 6 on both sides,
6×2/3 y = 6 × 5 – 6 × 1/2 x
2 × 2y = 30-3x
4y = 30-3x
y = 30-3x/4
y = 30/4 – 3/4 x
y = 15/2 – 3/4 x
Put x = 4
y = 15/2 – 3
y = 15-6/2
= 9/2
y = 4.5
Put x = 0
y = 15/2
y = 7.5
Put x = (-1)
Put = 15/2 + 3/4
y = 7.5 + 0.75
y = 8.25
X | 4 | 0 | 1==-1 |
y | 4.5 | 7.5 | 8.25 |
The co-ordinates of the points which are meet the co-ordinates at x-axis is (10, 0) and on-axis is (0, 7.5)
(iv) 2x-1/3 – y-2/5 =
Solution:
2x-1/3 – y-2/5 = 0
(2x-1)/3 = (y-2)/5
5 (2x – 1) = 3 (y – 2)
10x – 5 = 3y – 6
10x = 3y – 6 + 5
10x – 3y = -1
– 3y = -1 – 10x
y = -1-10x/-3
y = (-1) (1 + 10x)/-3
y = 1 + 10x/3
y = 1/3 + 10/3 x
Put x = 0
y = 1/3
y = 0.3
Put x = 3
y = 1/3 + 10
y = 1+30/3
y = 31/3 = y = 10.3
Put x = -1
y = 1/3 + 10/3 (-1)
y = 1/3 – 10/3
y = 1/3 – 10/3
y = 1-10/3
y = -9/3
y = -3
X | 0 | 3 | -1 |
y | 0.3 | 10.3 | -3 |
The co-ordinates meets at x-axis is (-0.1,0) and on y-axis is (0, 0.3)
(Q5) For each linear equation, given below, draw the graph and then use the graph drawn (in each case) to find the area of a triangle enclosed by the graph and the co-ordinates axes:
(i) 3x – (5 – y) = 7
(ii) 7 – 3 (1 – y) = -5 + 2x
solution:
(i) 3x – (5 – y) = 7
3x – 5 + y = 7
3x + y = 7 + 5
3x + y = 12
y = 12 – 3x
Put x = 0
y = 12
Put x = 4
y = 12 – 12
y = 0
∴ Area of △AOB = 1/2 × Base × height
= 1/2 × 4 × 12
= 4 × 6
= 24 sq. units
(ii) 7 – 3 (1 – y) = – 5 + 2x
Solution:
7 – 3 (1 – y) = -5 + 2x
7 – 3 + 3y = – 5 + 2x
4 + 3y = – 5 + 2x
3y = – 5 + 2x
3y = -9 + 2x
y = -9+2x/3
y = -9/3 + 2/3 x
y = -3 + 2/3 x
Put x = 0, y = -3
Put x = 3
y = -3 + 2
y = -1
Put x = +9/2
y = -3 + 2/3 (+9/2)
= -3 + 3
y = 0
Area of △AOB
1/2 × Base × Height
= 1/2 × AO × OB
= 1/2 × 4.5 × 3
= 3/2 × 4.5
= 1.5 × 4.5
= 675 sq.units
Here is your solution of Selina Concise Class 9 Maths Chapter 26 Co-ordinate Geometry Exercise 26B
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