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Distance Between Two Points Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Distance formula
The formula to calculate the distance between two points (x₁, y₁) and (x₂, y₂) is √((x₂ - x₁)² + (y₂ - y₁)²).
What does (x₁, y₁) represent?
(x₁, y₁) represents the coordinates of the first point.
What does (x₂, y₂) represent?
(x₂, y₂) represents the coordinates of the second point.
Why square the differences in the distance formula?
Squaring ensures the differences are positive and avoids cancelling out negative values.
What does the square root in the distance formula do?
The square root converts the squared distance back to the actual distance.
What is the distance between (3, 4) and (7, 1)?
Using the formula: √((7 - 3)² + (1 - 4)²) = √(4² + (-3)²) = √(16 + 9) = √25 = 5.
What is the distance between (0, 0) and (5, 12)?
Using the formula: √((5 - 0)² + (12 - 0)²) = √(5² + 12²) = √(25 + 144) = √169 = 13.
What is the distance between two points on a horizontal line?
The distance is the absolute difference between the x-coordinates, as the y-coordinates are the same.
What is the distance between two points on a vertical line?
The distance is the absolute difference between the y-coordinates, as the x-coordinates are the same.
How is the distance formula related to Pythagoras' Theorem?
The distance formula is derived from Pythagoras' Theorem, where the differences in x and y are the lengths of the two shorter sides of a right-angled triangle.
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