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

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

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

In this case, the coordinates for point A are (−7, 6) and for point B are (8, −5). Substituting these values into the formula:

1. Identify the coordinates:

   • For A: $(x_1, y_1) = (-7, 6)$
   • For B: $(x_2, y_2) = (8, -5)$

2. Calculate the differences:

   • $x_2 - x_1 = 8 - (-7) = 8 + 7 = 15$
   • $y_2 - y_1 = -5 - 6 = -11$

3. Substitute into the distance formula: $d = \sqrt{(15)^2 + (-11)^2}$ $d = \sqrt{225 + 121}$ $d = \sqrt{346}$

4. Calculate the square root: $d \approx 18.6$

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