Lines in Two Dimensions — Telangana (SSC) Class 10 Mathematics Solutions (Free)

Free step-by-step Telangana (SSC) Class 10 Mathematics solutions for "Lines in Two Dimensions" — important questions with detailed answers, download PDF for board exam preparation.

Lines in Two Dimensions — Telangana (SSC) Class 10 Mathematics Solutions (Free)

Free step-by-step Telangana (SSC) Class 10 Mathematics solutions for "Lines in Two Dimensions" — important questions with detailed answers, download PDF for board exam preparation.

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TL;DR: Free step-by-step Telangana (SSC) Class 10 Mathematics solutions for "Lines in Two Dimensions" — important questions with detailed answers, download P…

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Lines in Two Dimensions — Textbook Questions Answered (8)

Q1: Find the distance between points A(3, 4) and B(6, 8).

Step 1: Use distance formula d = √[(x₂ - x₁)² + (y₂ - y₁)²] Step 2: d = √[(6 - 3)² + (8 - 4)²] Step 3: d = √[3² + 4²] Step 4: d = √[9 + 16] = √25 = 5 Final Answer: Distance = 5 units

Q2: Find the slope of the line passing through points P(-2, 3) and Q(4, 6).

Step 1: Use slope formula m = (y₂ - y₁)/(x₂ - x₁) Step 2: m = (6 - 3)/(4 - (-2)) Step 3: m = 3/6 = 1/2 Final Answer: Slope = 1/2

Q3: Find the equation of the line passing through (2, 3) with slope 2.

Step 1: Use point-slope form: y - y₁ = m(x - x₁) Step 2: y - 3 = 2(x - 2) Step 3: y - 3 = 2x - 4 Step 4: y = 2x - 1 Final Answer: Equation is y = 2x - 1 or 2x - y - 1 = 0

Q4: Find the equation of the line passing through points (1, 2) and (3, 6).

Step 1: Find slope m = (6 - 2)/(3 - 1) = 4/2 = 2 Step 2: Use point-slope form with point (1, 2): y - 2 = 2(x - 1) Step 3: y - 2 = 2x - 2 Step 4: y = 2x Final Answer: Equation is y = 2x or 2x - y = 0

Q5: Check if the points A(0, -1), B(2, 1), and C(4, 3) are collinear.

Step 1: Find slope of AB: m₁ = (1 - (-1))/(2 - 0) = 2/2 = 1 Step 2: Find slope of BC: m₂ = (3 - 1)/(4 - 2) = 2/2 = 1 Step 3: Since m₁ = m₂ = 1, the slopes are equal Step 4: Points lie on the same line y = x - 1 Final Answer: Yes, the points are collinear

Q6: Find the midpoint of the line segment joining A(2, 4) and B(8, 10).

Step 1: Use midpoint formula M = ((x₁ + x₂)/2, (y₁ + y₂)/2) Step 2: M = ((2 + 8)/2, (4 + 10)/2) Step 3: M = (10/2, 14/2) = (5, 7) Final Answer: Midpoint = (5, 7)

Q7: Find the equation of a line parallel to y = 3x + 2 passing through (1, 4).

Step 1: Parallel lines have equal slopes Step 2: Slope of given line = 3 Step 3: Required line has slope = 3 Step 4: Use point-slope form: y - 4 = 3(x - 1) Step 5: y - 4 = 3x - 3 Step 6: y = 3x + 1 Final Answer: Equation is y = 3x + 1 or 3x - y + 1 = 0

Q8: Find the equation of a line perpendicular to y = 2x - 3 passing through (2, 5).

Step 1: Slope of given line = 2 Step 2: Slope of perpendicular line = -1/2 (negative reciprocal) Step 3: Use point-slope form: y - 5 = (-1/2)(x - 2) Step 4: y - 5 = -x/2 + 1 Step 5: y = -x/2 + 6 or x + 2y - 12 = 0 Final Answer: Equation is x + 2y - 12 = 0

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