Higher November 2023 Paper 2 Q12
12 \(A\) is the point with coordinates \((7, 13)\)
\(B\) is the point with coordinates \((-3, 21)\)
\(C\) is the point with coordinates \((15, 23)\)
\(M\) is the midpoint of \(AB\).
\(N\) is the midpoint of \(BC\).
Work out the distance between \(M\) and \(N\).
Give your answer correct to 1 decimal place. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 6.4 | P1 | for a suitable start to the process, eg, \(M = \left(\dfrac{7 - 3}{2}, \dfrac{13 + 21}{2}\right)\ (= (2, 17))\) or \(N = \left(\dfrac{15 - 3}{2}, \dfrac{23 + 21}{2}\right)\ (= (6, 22))\) |
| P1 | (dep on P1) for a correct first step using of Pythagoras, eg \((x_N - x_M)^2 + (y_N - y_M)^2\) eg \((\text{``}6\text{''} - \text{``}2\text{''})^2 + (\text{``}22\text{''} - \text{``}17\text{''})^2\ (= 41)\) | |
| A1 | for answer in the range 6.4 to 6.41 |
Additional guidance
Condone missing brackets on coordinates
Ignore units throughout
If an answer is given in the range in working and then rounded incorrectly award full marks.