Higher January 2020 Paper 2R Q24
24 L\(_1\) and L\(_2\) are two straight lines.
The origin of the coordinate axes is \(O\).
L\(_1\) has equation \(\;5x + 10y = 8\)
L\(_2\) is perpendicular to L\(_1\) and passes through the point with coordinates (8, 6)
L\(_2\) crosses the \(x\)-axis at the point \(A\).
L\(_2\) intersects the straight line with equation \(\;x = -3\;\) at the point \(B\).
Find the area of triangle \(AOB\).
Show your working clearly.
(5)
| Scheme | Marks |
|---|---|
| Gradient of L\(_2\) = (−10 ÷ −5) (= 2) | M1 |
| \(6 = 2 \times 8 + c \;\rightarrow\; c = -10\) \(y = 2x - 10\) oe | A1 |
| \(0 = 2x - 10 \;\rightarrow\; x = 5\) or (5, 0) \(y = 2 \times -3 - 10 \;\rightarrow\; y = -16\) or (−3, −16) | A1 |
(Area =) 0.5 × 5 × 16 or (0.5 × 5 × 10) + (0.5 × 10 × 3) or 0.5 × 5 × \(\sqrt{265}\) × sin 100.6° or 0.5 × \(\sqrt{320}\) × \(\sqrt{265}\) × sin 15.9° | M1 |
| Working required Answer: 40 | A1 cao |
| (5) | |
| (5 marks) |
Notes
M1: Method to find gradient of L\(_2\)
A1: Equation for L\(_2\)
A1: Finding point \(A\) and point \(B\)
M1: Method to find area of triangle
A1 cao: Dep on M2