4MA0 Higher January 2016 Paper 3R Q9
9 The point \(A\) has coordinates (0, 2)
The point \(B\) has coordinates (–4, –1)
(a) Find the coordinates of the midpoint of \(AB\). (2)
(b) Work out the gradient of the line \(AB\). (2)
(c) Find an equation of the line \(AB\). (2)
| Scheme | Marks |
|---|---|
| \(\left(\tfrac{1}{2}(0 - 4), \tfrac{1}{2}(2 - 1)\right)\) | M1 |
| \(\left(-2, \tfrac{1}{2}\right)\) | A1 |
| (2) |
Notes
M1: Accept \(\tfrac{1}{2}(0 - 4)\) or \(\tfrac{1}{2}(2 - 1)\) or one correct coordinate or \(\left(\tfrac{1}{2}, -2\right)\)
| Scheme | Marks |
|---|---|
| \(\dfrac{2 - (-1)}{0 - (-4)}\) or \(\dfrac{-1 - 2}{-4 - 0}\) oe | M1 |
| \(\dfrac{3}{4}\) | A1 |
| (2) |
Notes
M1: Award M1 for \(-\dfrac{3}{4}\) or \(\dfrac{3}{4}x\)
A1: Accept \(\dfrac{3}{4}\) or 0.75
| Scheme | Marks |
|---|---|
| \(y = \text{"}\tfrac{3}{4}\text{"}x + c\) or \(y = mx + 2\) oe | M1 |
| \(y = \tfrac{3}{4}x + 2\) oe | A1ft |
| (2) |
Notes
M1: \(c\) or \(m\) may be letters or any number except \(c = 0\), \(m = 0\) or \(m = 1\)
A1ft: Accept \(y - -1 = \dfrac{\text{"}3\text{"}}{4}(x - -4)\) oe
Award M1 A0 for \(\dfrac{\text{"}3\text{"}}{4}x + 2\)