Distance Formula

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Distance = √[(x₂ - x₁)² + (y₂ - y₁)²] This formula is derived using Pythagoras' theorem and gives the straight-line distance between any two points in a coordinate plane.

Answer

The Distance Formula is derived using Pythagoras' theorem: 1. Draw a right triangle with the two points as vertices 2. The horizontal side = |x₂ - x₁| 3. The vertical side = |y₂ - y₁| 4. Apply Pythago

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Distance from origin = √[x² + y²] This is a special case of the distance formula where one point is (0, 0) and the other is (x, y).

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Given: (x₁, y₁) = (3, 6) and (x₂, y₂) = (0, 2) Distance = √[(0 - 3)² + (2 - 6)²] = √[(-3)² + (-4)²] = √[9 + 16] = √25 = 5 units Answer: 5 units

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Distance from origin = √[x² + y²] = √[(-12)² + (5)²] = √[144 + 25] = √169 = 13 units Answer: 13 units

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• Point on x-axis: (x, 0) - ordinate is zero Examples: (3, 0), (-5, 0) • Point on y-axis: (0, y) - abscissa is zero Examples: (0, 4), (0, -7) This is important when solving problems involving di

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Let the point on x-axis be (x, 0) Distance = 5 5 = √[(x - 6)² + (0 - (-3))²] 5 = √[(x - 6)² + 9] 25 = (x - 6)² + 9 16 = (x - 6)² x - 6 = ±4 x = 10 or x = 2 Answer: (2, 0) and (10, 0)

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A point P is equidistant from points A and B if: PA = PB (distances are equal) This concept is used to: • Find points on perpendicular bisectors • Locate circumcenters of triangles • Solve geometric