1MA0 Higher June 2015 Paper 1 Q15
15 \(A\) and \(B\) are two points.
Point \(A\) has coordinates \((-2, 4)\).
Point \(B\) has coordinates (8, 9).
\(C\) is the midpoint of the line segment \(AB\).
(a) Find the coordinates of \(C\). (2)
\(D\) is the point with coordinates (100, 56).
*(b) Does point \(D\) lie on the straight line that passes through \(A\) and \(B\)?
You must show how you work out your answer. (3)
You must show how you work out your answer. (3)
| Answer | Mark | Notes |
|---|---|---|
| (3, 6.5) | 2 | M1 for a method to find either the \(x\) coordinate or the \(y\) coordinate of the midpoint or \(x = 3\) or \(y = 6.5\) oe A1 cao [SC: B1 for (6.5, 3)] |
| Answer | Mark | Notes |
|---|---|---|
| No and correct working | 3 | M1 for a method to work out a gradient between any relevant pair of points (ie 2 of points A, B, C or D), eg. \(\dfrac{9 - 4}{8 - {-2}} \left(= \dfrac{5}{10}\right)\) M1 (dep) for a method to work out the gradient between another pair of points which can be used for comparison; one gradient must be through D. C1 for “no” and a correct explanation based on two correct gradients OR M1 for a method to work out a gradient between any relevant pair of points (ie 2 of points A, B, C or D), eg. \(\dfrac{9 - 4}{8 - {-2}} \left(= \dfrac{5}{10}\right)\) M1 (dep) for using their gradient to work out an equation of a straight line in the form \(y = mx + c\) and substituting in an appropriate point C1 for “no” and a correct explanation based on correct working OR M2 for (100, 55) or (102, 56) C1 for “no” and a correct explanation based on correct coordinates. |