1MA0 Higher November 2014 Paper 1 Q24
*24 \(A\) is the point with coordinates (1, 3)
\(B\) is the point with coordinates \((4, -1)\)
The straight line \(\mathbf{L}\) goes through both \(A\) and \(B\).
Is the line with equation \(2y = 3x - 4\) perpendicular to line \(\mathbf{L}\)?
You must show how you got your answer. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(2y = 3x - 4\) \(y = \tfrac{3}{2}x - 2\); \(m = \tfrac{3}{2}\) \(\dfrac{-1 - 3}{4 - 1} = \dfrac{-4}{3}\) \(\tfrac{3}{2} \times \dfrac{-4}{3} = -2\) | No with reason | 4 | M1 for \(\tfrac{3}{2}\) oe or \(y = \tfrac{3}{2}x \left(-\tfrac{4}{2}\right)\) oe M1 for method to find gradient of AB, eg \(\dfrac{-1 - 3}{4 - 1}\) or \(\dfrac{3 - -1}{1 - 4}\) or \(\dfrac{-4}{3}\) oe A1 for identifying gradients as \(\tfrac{3}{2}\) oe and \(-\tfrac{4}{3}\) oe C1 (dep on M1) for a conclusion with a correct reason, eg No as product of \(\tfrac{3}{2}\) and \(\dfrac{-4}{3}\) is not \(-1\), ft from their two gradients |