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.
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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.
- A line passes through (1, 2) and makes an angle of 45° with the positive x-ax…
- Find the equation of the line which is perpendicular to x + 2y = 5 and passes…
- Find the equation of the line parallel to 2x - 3y + 7 = 0 and passing through…
- + 2 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 |
| A line passes through (1, 2) and makes an angle of 45° wi… | ✓ Solved |
| Find the equation of the line which is perpendicular to x… | ✓ Solved |
| Find the equation of the line parallel to 2x - 3y + 7 = 0… | ✓ Solved |
Showing 6 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 Answer: The equation is y = 2x - 1 or 2x - y - 1 = 0
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|/√25
Distance = 20/5
Distance = 4 units
Final Answer: The distance is 4 units
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: Since denominator is 0 (m₁m₂ = -1), the lines are perpendicular.
Angle θ = 90°
Final Answer: The lines are perpendicular; angle = 90°
Q4: A line passes through (1, 2) and makes an angle of 45° with the positive x-axis. Find its equation.
Given: Point (1, 2) and angle with x-axis = 45°
Step 1: Find the slope using the angle:
tan 45° = m
m = 1
Step 2: Use point-slope form:
y - y₁ = m(x - x₁)
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x + 1
Step 3: Write in standard form:
x - y + 1 = 0
Final Answer: The equation is y = x + 1 or x - y + 1 = 0
Q5: Find the equation of the line which is perpendicular to x + 2y = 5 and passes through (0, 0).
Given line: x + 2y = 5
Required line passes through origin (0, 0) and is perpendicular to the given line.
Step 1: Find the slope of the given line:
x + 2y = 5
2y = -x + 5
y = -x/2 + 5/2
Slope m₁ = -1/2
Step 2: Find the slope of perpendicular line:
For perpendicular lines: m₁ × m₂ = -1
(-1/2) × m₂ = -1
m₂ = 2
Step 3: Use point-slope form with (0, 0):
y - 0 = 2(x - 0)
y = 2x
Step 4: Write in standard form:
2x - y = 0
Final Answer: The equation is y = 2x or 2x - y = 0
Q6: Find the equation of the line parallel to 2x - 3y + 7 = 0 and passing through (3, 1).
Given line: 2x - 3y + 7 = 0
Required line is parallel and passes through (3, 1).
Step 1: Find the slope of the given line:
2x - 3y + 7 = 0
-3y = -2x - 7
y = (2/3)x + 7/3
Slope m = 2/3
Step 2: Parallel lines have equal slopes:
Required slope = 2/3
Step 3: Use point-slope form:
y - 1 = (2/3)(x - 3)
3(y - 1) = 2(x - 3)
3y - 3 = 2x - 6
2x - 3y - 3 = 0
Final Answer: The equation is 2x - 3y - 3 = 0
Showing 6 of 8 questions. Visit the full page for complete solutions.
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