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

Every straight-line question in Class 11 Maths Chapter 9 starts with the same idea: slope. These questions apply the slope formula to test parallel and perpendicular lines, write equations from given information, and calculate distances between points.

Last Updated: September 23, 2026

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.

Frequently Asked Questions

How would you find the equation of a line passing through (2,3) with slope 4?
Using point slope form y minus 3 = 4(x minus 2), which simplifies to 4x minus y minus 5 = 0.

A ladder leans so its base is 3 m from a wall and its top touches the wall at 4 m height, what line represents the ladder?
Using intercept form x over 3 plus y over 4 = 1, which simplifies to 4x + 3y minus 12 = 0.

Written by Satish

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