AQA · Mathematics · 8300
GCSE Maths: Pythagoras on a graph
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Pythagoras on a graph (Corbettmaths Video 258), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What formula is used to calculate the distance between two points (x₁, y₁) and (x₂, y₂) on a coordinate graph?
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The distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²], which is derived from the Pythagorean theorem.
What is the distance between the points (5, 1) and (9, 6)?
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√41 ≈ 6.4. Using the distance formula: √[(9-5)² + (6-1)²] = √[16 + 25] = √41.
What is the distance between the points (0, 0) and (6, 8)?
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10. Using the distance formula: √[(6-0)² + (8-0)²] = √[36 + 64] = √100 = 10.
What is the distance between the points (−6, 2) and (8, 3)?
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√197 ≈ 14.04. Using the distance formula: √[(8-(-6))² + (3-2)²] = √[196 + 1] = √197.
What is the distance between the points (−4, 0) and (0, −4)?
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4√2 ≈ 5.66. Using the distance formula: √[(0-(-4))² + (-4-0)²] = √[16 + 16] = √32 = 4√2.
If the distance between points (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] gives 289 = 225 + (p-2)², so (p-2)² = 64, yielding p-2 = ±8.
If the distance between points (−3, −4) and (q, 5) is 15, what are the possible values of q?
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q = 6 or q = -12. Using 15 = √[(q-(-3))² + (5-(-4))²] gives 225 = (q+3)² + 81, so (q+3)² = 144, yielding q+3 = ±12.
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