Foundation June 2022 Paper 2 Q25
25 The points \(L\), \(M\) and \(N\) are such that \(LMN\) is a straight line.
The coordinates of \(L\) are \((-3, 1)\)
The coordinates of \(M\) are \((4, 9)\)
Given that \(LM : MN = 2 : 3\),
find the coordinates of \(N\). (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 14.5, 21 | P1 | for process to work with coordinates, eg \(4 - (-3)\ (= 7)\) or \(9 - 1\ (= 8)\) |
| P1 | for process to use ratio, eg \(\text{``}7\text{''} \div 2\ (= 3.5)\) or \(\text{``}8\text{''} \div 2\ (= 4)\) or \(\text{``}7\text{''} \times 3\ (= 21)\) or \(\text{``}8\text{''} \times 3\ (= 24)\) | |
| P1 | for complete process to find either the \(x\) or the \(y\) coordinate of \(N\), eg \(\text{``}3.5\text{''} \times 3 + 4\) or \(\text{``}4\text{''} \times 3 + 9\) or \(\text{``}3.5\text{''} \times 5 - 3\) or \(\text{``}4\text{''} \times 5 + 1\) OR to find both the required distances eg \(\text{``}3.5\text{''} \times 3\ (= 10.5)\) and \(\text{``}4\text{''} \times 3\ (= 12)\) or \(\text{``}21\text{''} \div 2\ (= 10.5)\) and \(\text{``}24\text{''} \div 2\ (= 12)\) or \(\text{``}3.5\text{''} \times 5\ (= 17.5)\) and \(\text{``}4\text{''} \times 5\ (= 20)\) | |
| A1 | oe |
Additional guidance
Accept in reverse order eg \(-3 - 4\ (= -7)\) and negative distances throughout
This mark is implied by 10.5 or 12 or 17.5 or 20