Coordinates

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Coordinates are a pair of numbers (x, y) that specify the exact location of a point in a plane. They are determined by: • Drawing two perpendicular lines called axes of coordinates • The horizontal li…

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Step-by-step solution: • Point A: 3 units right (+3), 2 units up (+2) → A(3, 2) • Point B: 4 units left (-4), 1 unit up (+1) → B(-4, 1) • Point C: 2 units right (+2), 3 units down (-3) → C(2, -3) • Po…

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• Points on x-axis: y-coordinate = 0 Examples: (5, 0), (-3, 0), (0, 0) • Points on y-axis: x-coordinate = 0 Examples: (0, 4), (0, -2), (0, 0) • The origin (0, 0) lies on both axes Reason: Points …

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The line joining (2, 5) and (7, 5) is parallel to the x-axis. Reason: • Both points have the same y-coordinate (5) • When y-coordinates are equal, points lie on a horizontal line • Horizontal lines a…

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Step-by-step solution: Given opposite vertices: A(1, 2) and C(5, 6) Step 1: For rectangle with sides parallel to axes, other vertices are: • One vertex has same x as A, same y as C • Other vertex has…

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Distance Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²] Derivation: • Consider points A(x₁, y₁) and B(x₂, y₂) • Form a right triangle with these points • Horizontal leg length = |x₂ - x₁| • Vertical leg len…

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Step-by-step solution: Given: A(-3, 4) and B(2, -1) Step 1: Apply distance formula d = √[(x₂ - x₁)² + (y₂ - y₁)²] Step 2: Substitute values • x₁ = -3, y₁ = 4 • x₂ = 2, y₂ = -1 d = √[(2 - (-3))² + (-…

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Distance from point (x, y) to origin (0, 0): Using distance formula: d = √[(x - 0)² + (y - 0)²] d = √[x² + y²] Therefore: Distance = √(x² + y²) Examples: • Point (3, 4): Distance = √(3² + 4²) = √25…