AQA · Mathematics · 8300
GCSE Maths: Coordinates: distance between 2 points
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Coordinates: distance between 2 points (Corbettmaths Video 88), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is the formula for the distance between two points (x₁, y₁) and (x₂, y₂)?
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d = √[(x₂ − x₁)² + (y₂ − y₁)²]
Calculate the distance between the points (5, 1) and (9, 6).
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√41 (or approximately 6.40). Using d = √[(9−5)² + (6−1)²] = √[16 + 25] = √41.
Calculate the distance between the points (0, 0) and (6, 8).
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10. Using d = √[(6−0)² + (8−0)²] = √[36 + 64] = √100 = 10.
Calculate the distance between the points (−6, 2) and (8, 3).
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√197 (or approximately 14.04). Using d = √[(8−(−6))² + (3−2)²] = √[196 + 1] = √197.
Calculate the distance between the points (−5, −9) and (−3, 8).
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√293 (or approximately 17.12). Using d = √[(−3−(−5))² + (8−(−9))²] = √[4 + 289] = √293.
Calculate the distance between the points (−4, 0) and (0, −4).
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4√2 (or approximately 5.66). Using d = √[(0−(−4))² + (−4−0)²] = √[16 + 16] = √32 = 4√2.
The distance formula d = √[(x₂ − x₁)² + (y₂ − y₁)²] is derived from ?.
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Pythagoras' theorem
If the distance between (1, 2) and (16, p) is 17, what are the possible values of p?
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p = 10 or p = −6. Using 17 = √[(16−1)² + (p−2)²], we get 289 = 225 + (p−2)², so (p−2)² = 64, giving p−2 = ±8.
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