Higher June 2019 Paper 1 Q23
23 \(ABCD\) is a kite with \(AB = AD\) and \(CB = CD\).
\(B\) is the point with coordinates (10, 19)
\(D\) is the point with coordinates (2, 7)
Find an equation of the line \(AC\).
Give your answer in the form \(py + qx = r\) where \(p\), \(q\) and \(r\) are integers.
(5)
| Scheme | Marks |
|---|---|
| \(\left(\dfrac{10 + 2}{2}, \dfrac{7 + 19}{2}\right)\) or (6, 13) | M1 |
| \(\dfrac{19 - 7}{10 - 2}\left(= \dfrac{12}{8}\right)\) oe or 1.5 oe | M1 |
| \(m \times \dfrac{3}{2} = -1\) oe or \(m = -\dfrac{2}{3}\) | M1 |
\(\text{``}{13}\text{''} = \text{``}{-\dfrac{2}{3}}\text{''} \times \text{``}{6}\text{''} + c\) or \(c = 17\) oe or \(y - \text{``}{13}\text{''} = \text{``}{-\dfrac{2}{3}}\text{''}(x - \text{``}{6}\text{''})\) | M1 |
| \(3y + 2x = 51\) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for use of \(m_1m_2 = -1\)
M1: Or for \(y = -\dfrac{2}{3}x + 17\)
[NB: “13”, “6” and “\(-\dfrac{2}{3}\)” must come from correct working]
A1: for \(3y + 2x = 51\) or \(3y = -2x + 51\) etc but must be integer coefficients