Higher November 2021 Paper 2 Q11
11 Here is a sketch of the line L.
The points \(P(-6, 0)\) and \(Q(0, 3)\) are points on the line L.
The point \(R\) is such that \(PQR\) is a straight line and \(PQ : QR = 2 : 3\)
(a) Find the coordinates of \(R\). (2)
(b) Find an equation of the line that is perpendicular to L and passes through \(Q\). (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| (9, 7.5) | M1 | for \(x\) coordinate \(= PO\ (6) \times \dfrac{3}{2}\ (= 9)\) or \(y\) coordinate \(= OQ\ (3) \times \dfrac{5}{2}\ (= 7.5)\) or \(PO\ (6) \times \dfrac{5}{2}\ (= 15)\) or \(OQ\ (3) \times \dfrac{3}{2}\ (= 4.5)\) |
| A1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| \(y = -2x + 3\) | P1 | for process to find the gradient of the line, eg \(3 \div 6\ (= 0.5)\) or \(y = mx + 3\) |
| P1 | for process to find gradient of perpendicular eg \(-1 \div [\text{gradient of } PQ]\ (= -2)\) | |
| A1 | for \(y = -2x + 3\) oe |
Additional guidance
Could use \(P\) and \(R\) or \(Q\) and \(R\) as ft from (a)