Question

Based on the above information answer the following .

(i) The slope of line AB is

(a) 2 (b) 1 (c) ½ (d) 1/3

(ii) The equation of the line AB is

(a) x + 2y =1791 (b) x -2y = 1801 (c) x -2y =1791 (d) x -2y + 1801=0

(iii)the population in year 2010 is

(a) 104.5 (b) 119.5 (c) 109.5 (d) none of these

(iv) The equation of the line perpendicular to line AB and passing through (1995, 97) is

(a) 2x – y = 4087 (b) 2x + y = 4087 (c) 2x + y = 1801 (d) none of these

(v) In which year the population becomes 110 crores is

(a) 2020 (b) 2019 (c) 2021 (d) 2022

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Answer 1

Answer:

(a) 2 (b) 1 (c) ½ (d) 1/3

(ii) The equation of the line AB is

(a) x + 2y =1791 (b) x -2y = 1801 (c) x -2y =1791 (d) x -2y + 1801=0

(iii)the population in year 2010 is

Answer 2

(i) c, (ii) b, (iii) a, (iv) b, (v) c.

Given:

(i) The slope of line AB is

(a) 2 (b) 1 (c) ½ (d) 1/3

(ii) The equation of the line AB is

(a) x + 2y =1791 (b) x -2y = 1801 (c) x -2y =1791 (d) x -2y + 1801=0

(iii)the population in year 2010 is

(a) 104.5 (b) 119.5 (c) 109.5 (d) none of these

(iv) The equation of the line perpendicular to line AB and passing through (1995, 97) is

(a) 2x – y = 4087 (b) 2x + y = 4087 (c) 2x + y = 1801 (d) none of these

(v) In which year the population becomes 110 crores is

(a) 2020 (b) 2019 (c) 2021 (d) 2022

Solution:

(i) Slope of line AB is = $\frac{y2 - y1}{x2 - x1}$

= $\frac{97-92}{1995-1985}$

= 5/10

= 1/2

(ii) Equation of line AB is,

⇒ y-y1 = m(x-x1)

∴ y - 92 = 1/2(x - 1985)

2y - 184 = x - 1985

⇒ x - 2y = 1801

(iii) The population in 2010 be P.

Since A,B and C are collinear

∴ slope of AB = slope of BC

$\frac{97-92}{1995-1985} = \frac{P - 97}{2010 - 1995}$

⇒ $\frac{1}{2} = \frac{P - 97}{15}$

⇒ 7.5 = P - 97

⇒ P = 97 + 7.5 = 104.5 crores

(iv) ∵ Slope of AB = 1/2

Slope of the perpendicular of AB = $\frac{-1}{1/2}$ = -2

∴ Equation of line perpendicular to AB passing through (1995,97) is

⇒ y - 97 = -2(x - 1995)

⇒ y - 97 = -2x + 3990

⇒ 2x + y = 4087

(v) Equation of line AB is,

x -2y = 1801

Putting y =110,

∴ x = 1801+220

⇒ x = 2021

Therefore, population becomes 110 crores in 2021.

Hence, the correct options are (i) c, (ii) b, (iii) a, (iv) b, (v) c.

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