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.
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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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
Showing 5 of 8 questions — full solutions on the page.