Class 11 Maths Chapter 9 Straight Lines – Extra Questions with Answers

Extra practice questions for Class 11 Maths Chapter 9 (Straight Lines), beyond the textbook. These Class 11 Maths Chapter 9 important questions are handy for last-minute exam practice.

Very Short Answer Questions (1 mark)

Q1. Find the slope of the line through (1,2) and (3,6).
Ans: m = (6−2)/(3−1) = 4/2 = 2.

Q2. What is the slope of a vertical line?
Ans: Undefined.

Q3. If two lines have slopes 2 and −1/2, are they perpendicular?
Ans: Yes, since 2 × (−1/2) = −1.

Q4. Write the equation of a line with slope 3 and y-intercept 5.
Ans: y = 3x + 5.

Q5. Find the distance between (0,0) and (3,4).
Ans: √(3²+4²) = √25 = 5.

Short Answer Questions (2–3 marks)

Q6. Find the equation of the line passing through (2,3) with slope 4, using the point-slope form.
Ans: y−3 = 4(x−2), which simplifies to y = 4x−5.

Q7. Find the distance of the point (3,4) from the line 3x+4y−10=0.
Ans: d = |3(3)+4(4)−10|/√(3²+4²) = |9+16−10|/5 = 15/5 = 3.

Q8. Find the equation of the line passing through (1,2) and (4,8), and determine its slope.
Ans: Slope m = (8−2)/(4−1) = 6/3 = 2. Using point-slope: y−2 = 2(x−1), giving y = 2x.

Higher-Order Thinking / Application Questions

Q9. Two lines are given: L1 with equation y=2x+3, and L2 passing through (0,1) and perpendicular to L1. Find the equation of L2, showing your reasoning.
Ans: L1 has slope 2. Since L2 is perpendicular to L1, its slope must satisfy m₁×m₂=−1, so m₂ = −1/2. Using point-slope form with point (0,1): y−1 = −1/2(x−0), giving y = −x/2 + 1.

Q10. A triangle has vertices at A(0,0), B(4,0), and C(2,3). Find the length of each side using the distance formula, and determine if the triangle is isosceles.
Ans: AB = √[(4−0)²+(0−0)²] = 4. BC = √[(2−4)²+(3−0)²] = √(4+9) = √13. AC = √[(2−0)²+(3−0)²] = √(4+9) = √13. Since BC = AC = √13 (equal), the triangle is isosceles.

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.