| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Equation of line through two points |
| Difficulty | Moderate -0.3 This is a multi-part coordinate geometry question requiring standard techniques (gradient, equation of line, perpendicularity check, area, midpoint) but with minimal problem-solving demand. Part (iii)'s insight about equidistance is accessible once you recognize D is the midpoint of the hypotenuse in a right-angled triangle. Slightly easier than average due to routine methods and straightforward calculations. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
10 Point A has coordinates (4, 7) and point B has coordinates (2, 1).\\
(i) Find the equation of the line through A and B .\\
(ii) Point C has coordinates ( $- 1,2$ ). Show that angle $\mathrm { ABC } = 90 ^ { \circ }$ and calculate the area of triangle ABC .\\
(iii) Find the coordinates of D , the midpoint of AC .
Explain also how you can tell, without having to work it out, that $\mathrm { A } , \mathrm { B }$ and C are all the same distance from D.
\hfill \mbox{\textit{OCR MEI C1 2012 Q10 [11]}}