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A and B are points on a centimetre grid - Edexcel - GCSE Maths - Question 13 - 2022 - Paper 2

Question 13

A and B are points on a centimetre grid. A is the point with coordinates (–7, 6) B is the point with coordinates (8, –5) Work out the length of AB. Give your answer... show full transcript

Worked Solution & Example Answer:A and B are points on a centimetre grid - Edexcel - GCSE Maths - Question 13 - 2022 - Paper 2

Step 1

Step 1: Calculate the distance formula

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Answer

To find the length of the line segment AB, we use the distance formula:

$d = ext{√}((x_2 - x_1)^2 + (y_2 - y_1)^2)$

Where

A with coordinates (x₁, y₁) = (–7, 6)

B with coordinates (x₂, y₂) = (8, –5)

Step 2

Step 2: Substitute the coordinates into the formula

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Answer

Substituting the coordinates into the distance formula gives:

$d = ext{√}((8 - (–7))^2 + ((–5) - 6)^2)$

This simplifies to:

$d = ext{√}((8 + 7)^2 + (–5 - 6)^2)$

$d = ext{√}(15^2 + (–11)^2)$

$d = ext{√}(225 + 121)$

$d = ext{√}(346)$

Step 3

Step 3: Calculate the final distance

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Answer

Now we evaluate $d = ext{√}(346)$ :

$d ≈ 18.6$

Thus, the length of AB is approximately 18.6 cm, rounded to 1 decimal place.

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