Mathematics Questions and Answers – Various Forms of the Equation of a Line

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This set of Mathematics Problems for Class 11 focuses on “Various Forms of the Equation of a Line”.

1. If slope of a line is positive then its inclination is ___________
a) right angle
b) acute angle
c) obtuse angle
d) zero
View Answer

Answer: b
Explanation: If inclination is α slope is given by tan α. Given that slope of line is positive which means tan α is positive. We know, tan α is positive in 1st quadrant i.e. α should be acute angle.
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2. If slope of a line is negative then its inclination is ___________
a) right angle
b) acute angle
c) obtuse angle
d) zero
View Answer

Answer: c
Explanation: If inclination is α slope is given by tan α. Given that slope of line is negative which means tan α is negative. We know, tan α is negative in 2nd quadrant i.e. α should be obtuse angle.

3. Find slope of line joining (1, 2) and (4, 11).
a) 1/3
b) 3
c) 9
d) 1/9
View Answer

Answer: b
Explanation: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by \(\frac{y_2-y_1}{x_2-x_1}\).
So, slope of line joining (1, 2) and (4, 11) is \(\frac{11-2}{4-1} = \frac{9}{3}\) = 3.
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4. If two lines are parallel their inclination angle may be different.
a) True
b) False
View Answer

Answer: b
Explanation: If two lines are parallel then they form same angle with positive direction of x-axis in anticlockwise direction i.e. their inclinations are equal.

5. If two lines are parallel then their slopes must be equal.
a) True
b) False
View Answer

Answer: a
Explanation: Let the inclination of the two lines be α and β. Since they are parallel so, α = β.
=>tan α = tan β. Hence their slopes are equal.
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6. If the two lines are perpendicular then difference of their inclination angle is ________
a) 45°
b) 60°
c) 90°
d) 180°
View Answer

Answer: c
Explanation: If the two lines are perpendicular then if one line form angle α with positive x-axis then the other line form angle 90°+ α.
mathematics-questions-answers-various-forms-equation-line-q6

7. If the two lines with slope m1 and m2 are perpendicular then their slopes has relation ______
a) m1 + m2 = 1
b) m1 * m2 = 1
c) m1 * m2 = -1
d) m1 + m2 = -1
View Answer

Answer: c
Explanation: If the two lines are perpendicular then if one line form angle α with positive x-axis then the other line form angle 90° + α.
If m1 = tan α then m2 will be tan (90°+ α) = – cot α = -1/tan α
=> m1 * m2 = – 1.
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8. If angle between the two lines is 45° and slope of one line is 1/4 then which of the following is possible value of the slope of other line.
a) 5/3
b) 3/5
c) -5/3
d) 4/5
View Answer

Answer: a
Explanation: If angle between two lines with slopes m1 and m2 is α then tan α = |(m1-m2)/(1+m1*m2)|
tan 450 = \(|\frac{m-1/4}{1+m/4}| = \frac{4m-1}{m+4}\)
=>1 = \(\frac{4m-1}{m+4}\) => m+4 = 4m-1 => 3m = 5
=>m = 5/3.

9. If angle between the two lines is 45° and slope of one line is 1/4 then which of the following is possible value of the slope of other line.
a) 3/5
b) -3/5
c) -5/3
d) 4/5
View Answer

Answer: b
Explanation: If angle between two lines with slopes m1 and m2 is α then tan α = |(m1-m2)/(1+m1*m2)|
tan 45° = \(|\frac{m-1/4}{1+m/4}|\)
=> \(\frac{4m-1}{m+4}\) = -1
=>- m-4 = 4m-1 => 5m = -3
=> m = -3/5.
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10. If slope of a line is 2/3 then find the slope of line perpendicular to it.
a) -3/2
b) 3/2
c) 2/3
d) -2/3
View Answer

Answer: a
Explanation: If lines with slopes m1 and m2 are perpendicular then m1 * m2 = – 1.
If m1 = 2/3 then m2 = -1 / (2/3) = -3/2.

11. If slope of one line is 1/4 and other is 5/3 then find the angle between two lines.
a) 30°
b) 45°
c) 90°
d) 180°
View Answer

Answer: b
Explanation: If angle between two lines with slopes m1 and m2 is α then tan α = |(m1-m2)/(1+m1*m2)|
tan α = \(|\frac{5/3-1/4}{1+5/3*1/4}| = |\frac{20-3}{12+5}|\) = 17/17 =1 => α = 45°

12. Find slope of line passing through origin and (3, 6).
a) 2
b) 3
c) 1/3
d) 1/2
View Answer

Answer: a
Explanation: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by (y2-y1)/(x2-x1).
So, slope of line joining (0, 0) and (3, 6) is (6-0)/(3-0) = 6/3 = 2.

13. If line joining (1, 2) and (5, 7) is parallel to line joining (3, 4) and (11, x).
a) 10
b) 11
c) 12
d) 14
View Answer

Answer: d
Explanation: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by(y2-y1)/(x2-x1).
Lines are parallel means slope is equal.
=>(x-4)/(11-3) = (7-2)/(5-1) => x-4 = 5*8/4 = 10 => x=14.

14. If line joining (1, 2) and (7, 6) is perpendicular to line joining (3, 4) and (11, x).
a) 12
b) 16
c) -16
d) -12
View Answer

Answer: c
Explanation: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by(y2-y1)/(x2-x1).
Lines are perpendicular means m1*m2 = -1
=> \((\frac{x-4}{11-3})(\frac{6-2}{7-1})\) = -1
=> (x-4)(4) = (-1)(8)(6)
=> x-4 = -12 => x= -16.

15. The points A (1, 2), B (3, 5), C (7, 8) are collinear.
a) True
b) False
View Answer

Answer: b
Explanation: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by(y2-y1)/(x2-x1).
Slope of line AB = (5-2)/(3-1) = 3/2
Slope of line BC = (8-5)/(7-3) = 3/4
Since slope of AB is not equal to BC so, points are not collinear.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter