Higher June 2023 Paper 2 Q9
9 A (1, 3) and B (2, 9) are points on a centimetre grid.
ABCD is a parallelogram.
AD and BC are horizontal and each has length 5 cm
The diagonals of ABCD cross at E.
Work out the two possible pairs of coordinates of E. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Identifies (6, 3) or (7, 9) or \((-4, 3)\) or \((-3, 9)\) | M1 | may be seen on the grid mark intention on diagram eg parallelogram drawn with one of the vertices at (6, 3) or (6, 3) plotted |
| Identifies (6, 3) and (7, 9) or identifies \((-4, 3)\) and \((-3, 9)\) | M1dep | may be seen on the grid mark intention on diagram eg parallelogram drawn with two of the vertices at (6, 3) and (7, 9) or (6, 3) and (7, 9) plotted |
| Both diagonals drawn for one of the correct parallelograms or centre of one of the correct parallelograms identified or (4, 6) or \((-1, 6)\) | M1dep | mark intention on diagram M3 may be implied eg \(\left(\dfrac{1 + 7}{2}, \dfrac{9 + 3}{2}\right)\) or \(\left(\dfrac{-4 + 2}{2}, \dfrac{9 + 3}{2}\right)\) |
| (4, 6) and \((-1, 6)\) | A1 |
Additional guidance
| Up to M3 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| Both answers correct (ignore working) | M3A1 |
| One answer correct (ignore working) | M3A0 |
| For first 2 marks condone correct points plotted even if labelled incorrectly | |
| Up to M2 can be awarded for coordinates given as answers | |
| Arc centre \(A\) radius 5 cm passing through (6, 3) and/or \((-4, 3)\) is not sufficient to award M1 etc |