Higher November 2018 Paper 2 Q18
18 The straight line \(\mathbf{L}_1\) passes through the points with coordinates \((4, 6)\) and \((12, 2)\)
The straight line \(\mathbf{L}_2\) passes through the origin and has gradient \(-3\)
The lines \(\mathbf{L}_1\) and \(\mathbf{L}_2\) intersect at point \(P\).
Find the coordinates of \(P\). (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\left(\dfrac{-16}{5}, \dfrac{48}{5}\right)\) | P1 | for a method to find gradient of \(\mathbf{L}_1\) eg \(\dfrac{6 - 2}{4 - 12}\ \left(= -\frac{1}{2}\right)\) or states \(\mathbf{L}_2\) as \(y = -3x\) |
| P1 | (dep on P1) for a method to find equation of \(\mathbf{L}_1\) eg subs into \(y = \text{``}{-}\frac{1}{2}\text{''}x + c\) OR states \(\mathbf{L}_1\) as \(y = \text{``}{-}\frac{1}{2}\text{''}x + 8\) | |
| P1 | (dep on P2) complete method to equate both lines eg \(\text{``}{-}\frac{1}{2}\text{''}x + 8 = -3x\) | |
| A1 | oe |
Additional guidance
Ignore sketches.
Accept equivalents eg \((-3.2, 9.6)\)