Higher November 2020 Paper 1 Q22
22 \(ABCD\) is a rhombus.
The diagonals, \(AC\) and \(BD\), intersect at the point \(M\).
The coordinates of \(M\) are \((6, -11)\)
The points \(A\) and \(C\) both lie on the line with equation \(2y + 7x = 20\)
Find the exact coordinates of the point where the line through \(B\) and \(D\) intersects the \(y\)-axis.
(4)
| Scheme | Marks |
|---|---|
| \(y = -\dfrac{7}{2}x\;(+10)\) or (gradient =) \(-\dfrac{7}{2}\) | B1 |
| \(\text{‘}-\dfrac{7}{2}\text{’}m = -1\) or \((m =)\; \text{‘}\dfrac{2}{7}\text{’}\) | M1 |
| \(-11 = \text{‘}\dfrac{2}{7}\text{’} \times 6 + c\) or \(y - {-11} = \text{‘}\dfrac{2}{7}\text{’}(x - 6)\) oe | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(\left(0, -\dfrac{89}{7}\right)\) | A1 |
| (4) | |
| (4 marks) |
Notes
B1: for correct gradient which may be seen in an equation.
Condone \(-\dfrac{7}{2}x\)
M1: ft their gradient for use of \(m_1 \times m_2 = -1\)
M1: ft dep on M1
A1: accept \(\left(0, -12\dfrac{5}{7}\right)\) must be exact values