Higher January 2021 Paper 1R Q22
22 \(ABC\) is an isosceles triangle with \(AB = AC\).
\(B\) is the point with coordinates \((-1, 5)\)
\(C\) is the point with coordinates \((2, 10)\)
\(M\) is the midpoint of \(BC\).
Find an equation of the line through the points \(A\) and \(M\).
Give your answer in the form \(py + qx = r\) where \(p\), \(q\) and \(r\) are integers.
(5)
| Scheme | Marks |
|---|---|
| \(\left(\dfrac{-1 + 2}{2}, \dfrac{5 + 10}{2}\right)\) or (0.5, 7.5) oe | M1 |
| \(\dfrac{10 - 5}{2 - (-1)}\left(= \dfrac{5}{3}\right)\) oe | M1 |
| \(m \times \text{‘}\dfrac{5}{3}\text{’} = -1\) oe or \(m = -\dfrac{3}{5}\) oe | M1 |
‘7.5’ = ‘\(-\dfrac{3}{5}\)’ × ‘0.5’ + \(c\) or \(c = 7.8\) oe or \(y - \text{‘}7.5\text{’} = \text{‘}-\dfrac{3}{5}\text{’}(x - \text{‘}0.5\text{’})\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(5y + 3x = 39\) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: ft their gradient for use of \(m_1 \times m_2 = -1\)
M1: ft dep on first M1 and third M1
A1: oe where \(p\), \(q\) and \(r\) must be integers