Foundation June 2025 Paper 3 Q28
28 \(ABC\) is a straight line.
Point \(A\) has coordinates \((2, 7)\)
Point \(B\) has coordinates \((8, 12)\)
\(BC = \dfrac{1}{2}AB\)
Find the coordinates of point \(C\). (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| (11, 14.5) | P1 | for process to work with coordinates, eg \(8 - 2\ (= 6)\) or \(12 - 7\ (= 5)\) or eg \((2 + 8) \div 2\ (= 5)\) or \((7 + 12) \div 2\ (= 9.5)\) |
| P1 | for process to use proportion, eg \(\text{``}6\text{''} \div 2\ (= 3)\) oe or \(\text{``}5\text{''} \div 2\ (= 2.5)\) oe or \(2 + \text{``}6\text{''} \times 1.5\ (= 11)\) or \(2 + 9\ (= 11)\) oe or \(7 + \text{``}5\text{''} \times 1.5\ (= 14.5)\) or \(7 + 7.5\ (= 14.5)\) oe or \(\text{``}5\text{''} + \text{``}6\text{''}\ (= 11)\) or \(8 + \text{``}5\text{''} - 2\ (= 11)\) oe or \(\text{``}9.5\text{''} + \text{``}5\text{''}\ (= 14.5)\) or \(12 + \text{``}9.5\text{''} - 7\ (= 14.5)\) oe or \((11, a)\) where \(a \neq 14.5\) or \((b, 14.5)\) where \(b \neq 11\) | |
| A1 | for (11, 14.5) oe |
Additional guidance
Working may be seen on the diagram
Allow alternative notation
eg (6, 5) or (5, 6)
or (5, 9.5) or (9.5, 5)
Implied by \(\dfrac{\ldots\ldots}{8 - 2}\) or \(\dfrac{12 - 7}{\ldots\ldots}\) even if using \(\dfrac{\text{diff in } x}{\text{diff in } y}\)
Allow alternative notation
eg (3, 2.5) or (2.5, 3)
Implied by
\(8 + \text{``}3\text{''}\ (= 11)\) or \(12 + \text{``}2.5\text{''}\ (= 14.5)\)
Award P2 for (14.5, 11)