Higher November 2019 Paper 2 Q25
25 The straight line L has equation \(3x + 2y = 17\)
The point \(A\) has coordinates (0, 2)
The straight line M is perpendicular to L and passes through \(A\).
Line L crosses the \(y\)-axis at the point \(B\).
Lines L and M intersect at the point \(C\).
Work out the area of triangle \(ABC\).
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 9.75 | P1 | process to find the gradient of L \(\left(= -\dfrac{3}{2}\right)\) |
| P1 | process to find the gradient of the perpendicular line M eg use of \(-\dfrac{1}{m}\) or states gradient as \(\dfrac{2}{3}\) or \(y = \dfrac{2}{3}x + c\) | |
| B1 | (indep) gives \(y\) coordinate of \(B = 8.5\) oe | |
| P1 | (dep P2) process to find \(x\) coordinate of \(C\) (= 3) or \(y\) coordinate of \(C\) (= 4) eg the first stage of solving equations or using elimination by substitution, to find a coordinate of \(C\). | |
| A1 | 9.75 oe |
Additional guidance
Could be indicated other ways, eg 8.5 on the \(y\) axis of a diagram
ft their linear equation for M with L; allow some error in manipulation of these linear equations as long as the overall process is correct.
Award 0 marks for a correct answer with no supportive working.