Straight Lines — Class 11 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Straight Lines" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Straight Lines" — 8 important questions with detailed answers for CBSE board exam…
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Key Questions Covered:
- Find the equation of the line passing through points (2, 3) and (4, 7).
- Find the distance from the point (3, 4) to the line 3x + 4y - 5 = 0.
- Find the angle between the lines 2x + y - 3 = 0 and x - 2y + 4 = 0.
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the equation of the line passing through points (2, … | ✓ Solved |
| Find the distance from the point (3, 4) to the line 3x + … | ✓ Solved |
| Find the angle between the lines 2x + y - 3 = 0 and x - 2… | ✓ Solved |
Showing 3 of 8 questions
Q1: Find the equation of the line passing through points (2, 3) and (4, 7).
Given points: P₁(2, 3) and P₂(4, 7)
Step 1: Find the slope of the line:
m = (y₂ - y₁)/(x₂ - x₁) = (7 - 3)/(4 - 2) = 4/2 = 2
Step 2: Use the point-slope form:
y - y₁ = m(x - x₁)
Using point (2, 3):
y - 3 = 2(x - 2)
y - 3 = 2x - 4
y = 2x - 1
Step 3: Write in standard form:
2x - y - 1 = 0
Final Ans...
Q2: Find the distance from the point (3, 4) to the line 3x + 4y - 5 = 0.
Given point P(3, 4) and line 3x + 4y - 5 = 0
Line in form ax + by + c = 0 where a = 3, b = 4, c = -5
Step 1: Use the distance formula:
Distance = |ax₀ + by₀ + c|/√(a² + b²)
Step 2: Substitute the values:
Distance = |3(3) + 4(4) + (-5)|/√(3² + 4²)
Distance = |9 + 16 - 5|/√(9 + 16)
Distance = |20|/√...
Q3: Find the angle between the lines 2x + y - 3 = 0 and x - 2y + 4 = 0.
Line 1: 2x + y - 3 = 0, so m₁ = -2/1 = -2
Line 2: x - 2y + 4 = 0, so 2y = x + 4, m₂ = 1/2
Step 1: Use the angle formula:
tan θ = |(m₁ - m₂)/(1 + m₁m₂)|
Step 2: Calculate m₁m₂:
m₁m₂ = (-2)(1/2) = -1
Step 3: Substitute in the formula:
tan θ = |(-2 - 1/2)/(1 + (-1))|
tan θ = |(-5/2)/0|
Step 4: Sinc...
Showing 3 of 8 questions. Visit the full page for complete solutions.