4400 Higher June 2004 Paper 3 Q6
6 Two points, \(A\) and \(B\), are plotted on a centimetre grid.
\(A\) has coordinates \((2, 1)\) and \(B\) has coordinates \((8, 5)\).
(a) Work out the coordinates of the midpoint of the line joining \(A\) and \(B\). (2)
(b) Use Pythagoras’ Theorem to work out the length of \(AB\).
Give your answer correct to 3 significant figures. (4)
Give your answer correct to 3 significant figures. (4)
| Scheme | Marks |
|---|---|
| (5, 3) | B2 |
| (2) |
Notes
B2: B1 for each coordinate
| Scheme | Marks |
|---|---|
| 8 − 2 = 6 & 5 − 1 = 4 | B1 |
| \(6^2 + 4^2\) or 36 + 16 or 52 | M1 |
| \(\sqrt{6^2 + 4^2}\) or \(\sqrt{52}\) (7.2110…) | M1 |
| 7.21 | A1 |
| (4) | |
| (6 marks) |
Notes
M1: for squaring & adding
M1: (dep on 1st M1) for square root
A1: for 7.21 or better
M1 M1: either 6 or 4 must be correct for award of M marks