Straight Lines
Uttar Pradesh Board · Class 11 · Mathematics
Flashcards for Straight Lines — Uttar Pradesh Board Class 11 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
Find the slope of the line passing through points A(2, 3) and B(5, 9).
Answer
Step 1: Use slope formula m = (y₂ - y₁)/(x₂ - x₁) Step 2: Identify coordinates: (x₁, y₁) = (2, 3) and (x₂, y₂) = (5, 9) Step 3: Substitute values: m = (9 - 3)/(5 - 2) = 6/3 = 2 Answer: Slope = 2
Write the equation of a line with slope 3 passing through point (-1, 4).
Answer
Step 1: Use point-slope form: y - y₁ = m(x - x₁) Step 2: Given: m = 3, (x₁, y₁) = (-1, 4) Step 3: Substitute: y - 4 = 3(x - (-1)) Step 4: Simplify: y - 4 = 3(x + 1) Step 5: Expand: y - 4 = 3x + 3 Step
Find the equation of the line passing through points (1, 2) and (3, 8).
Answer
Step 1: Find slope: m = (8 - 2)/(3 - 1) = 6/2 = 3 Step 2: Use point-slope form with point (1, 2): y - 2 = 3(x - 1) Step 3: Expand: y - 2 = 3x - 3 Step 4: Simplify: y = 3x - 1 Verification: Check with
A line makes intercepts 4 and -6 on x and y axes respectively. Find its equation.
Answer
Step 1: Use intercept form: x/a + y/b = 1 Step 2: Given: a = 4 (x-intercept), b = -6 (y-intercept) Step 3: Substitute: x/4 + y/(-6) = 1 Step 4: Simplify: x/4 - y/6 = 1 Step 5: Convert to standard form
Find the distance from point P(3, 4) to the line 3x + 4y - 5 = 0.
Answer
Step 1: Use distance formula: d = |Ax₁ + By₁ + C|/√(A² + B²) Step 2: Identify: A = 3, B = 4, C = -5, (x₁, y₁) = (3, 4) Step 3: Substitute numerator: |3(3) + 4(4) + (-5)| = |9 + 16 - 5| = |20| = 20 Ste
Check if lines 2x + 3y - 6 = 0 and 4x + 6y - 12 = 0 are parallel, perpendicular, or neither.
Answer
Step 1: Find slopes by converting to y = mx + c form Line 1: 3y = -2x + 6 → y = -2x/3 + 2 → m₁ = -2/3 Line 2: 6y = -4x + 12 → y = -4x/6 + 2 → y = -2x/3 + 2 → m₂ = -2/3 Step 2: Compare slopes: m₁ = m₂
Find the acute angle between lines y = 2x + 1 and y = -x + 3.
Answer
Step 1: Identify slopes: m₁ = 2, m₂ = -1 Step 2: Use angle formula: tan θ = |(m₂ - m₁)/(1 + m₁m₂)| Step 3: Substitute: tan θ = |(-1 - 2)/(1 + 2(-1))| = |-3/(1 - 2)| = |-3/(-1)| = 3 Step 4: Find angle:
Find the perpendicular distance between parallel lines 3x + 4y - 7 = 0 and 3x + 4y + 8 = 0.
Answer
Step 1: Use distance formula for parallel lines: d = |C₁ - C₂|/√(A² + B²) Step 2: Identify: A = 3, B = 4, C₁ = -7, C₂ = 8 Step 3: Calculate numerator: |(-7) - 8| = |-15| = 15 Step 4: Calculate denomin
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