| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Equation of line through two points |
| Difficulty | Moderate -0.5 This is a straightforward multi-part coordinate geometry question requiring standard techniques (gradient, line equation, perpendicularity check, area, midpoint). Part (iii)'s conceptual insight about the circumcentre is slightly above pure recall, but overall this is easier than average due to simple arithmetic and routine methods. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.10f Distance between points: using position vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((1.5, 4.5)\) oe | 2 | B1 each coordinate |
| Angle in semicircle oe is a right-angle [so B is on circle] and must mention AC as diameter or D as centre [hence A, B, C all same distance from D] | E1 | Or '[since \(b = 90°\),] ABC are three vertices of a rectangle. D is the midpoint of one diagonal and so D is the centre of the rectangle or the diagonals of a rectangle are equal and bisect each other, [hence DA=DB=DC]'; or condone showing that line from D to mid point of AB is perp to AB, so DBA is isos [hence DB = DA = DC] [or equiv using DBC] |
## Question 1 (iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(1.5, 4.5)$ oe | 2 | B1 each coordinate |
| Angle in semicircle oe is a right-angle [so B is on circle] and must mention AC as diameter or D as centre [hence A, B, C all same distance from D] | E1 | Or '[since $b = 90°$,] ABC are three vertices of a rectangle. D is the midpoint of one diagonal and so D is the centre of the rectangle or the diagonals of a rectangle are equal and bisect each other, [hence DA=DB=DC]'; or condone showing that line from D to mid point of AB is perp to AB, so DBA is isos [hence DB = DA = DC] [or equiv using DBC] | E0 for just stating 'D is midpt of the hypotenuse of a rt angled triangle ABC so DAB is isos' without showing that it is; isw eg wrong calcn of radius; NB some wrongly asserting that ABC is isos |
---1 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 Q1 [11]}}