Higher January 2023 Paper 2 Q6
6 The points \(A\) and \(B\) are on a coordinate grid.
The coordinates of \(A\) are \((6, 4)\)
The coordinates of \(B\) are \((17, j)\;\) where \(j\) is a constant.
The midpoint of \(AB\) has coordinates \((k, 15)\;\) where \(k\) is a constant.
Find the value of \(j\) and the value of \(k\)
(3)
| Scheme | Marks |
|---|---|
\([k =]\;\dfrac{6 + 17}{2}\) or \([k =]\;6 + \dfrac{17 - 6}{2}\) oe or \([j =]\;4 + 2(15 - 4)\) or \([j =]\;15 + (15 - 4)\) or \(\dfrac{4 + j}{2} = 15\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(j = 26\) | A1 |
| \(k = 11.5\) | A1 |
| (3) | |
| (3 marks) |
Notes
A1: oe eg \(\dfrac{23}{2}\)
both answers the wrong way round scores M1A1 unless the correct answers are clearly labelled in working space
1 correct answer will score M1A1 and both will score M1A1A1