| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Verify shape type from coordinates |
| Difficulty | Moderate -0.8 This is a straightforward C1 coordinate geometry question requiring only basic gradient formula application, recognition that perpendicular lines have gradients with product -1, and simple area calculation using ½×base×height. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple connected steps. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks | Guidance |
|---|---|---|
| Grad \(AB = \frac{3-2}{1-(-2)} = \frac{1}{3}\); Grad \(BC = \frac{-3-3}{3-1} = \frac{-6}{2} = -3\) | B1 B1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Since \(\frac{1}{3} \times (-3) = -1\) the lines are perpendicular | B1 | |
| So the triangle is right-angled. | Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Distances \(= \sqrt{(3-2)^2+(1-{-2})^2} = \sqrt{1+9} = \sqrt{10}\) | M1 | |
| and \(\sqrt{(3-{-3})^2+(1-3)^2} = \sqrt{36+4} = \sqrt{40}\) | A1 | |
| \(\Rightarrow\) Area \(= \frac{1}{2}\sqrt{10}\cdot\sqrt{40} = 10\) | Total: 2 |
# Question 4:
## Part (i):
Grad $AB = \frac{3-2}{1-(-2)} = \frac{1}{3}$; Grad $BC = \frac{-3-3}{3-1} = \frac{-6}{2} = -3$ | B1 B1 | **Total: 2**
## Part (ii):
Since $\frac{1}{3} \times (-3) = -1$ the lines are perpendicular | B1 |
So the triangle is right-angled. | | **Total: 1**
## Part (iii):
Distances $= \sqrt{(3-2)^2+(1-{-2})^2} = \sqrt{1+9} = \sqrt{10}$ | M1 |
and $\sqrt{(3-{-3})^2+(1-3)^2} = \sqrt{36+4} = \sqrt{40}$ | A1 |
$\Rightarrow$ Area $= \frac{1}{2}\sqrt{10}\cdot\sqrt{40} = 10$ | | **Total: 2**
---4 The coordinates of the points $\mathrm { A } , \mathrm { B }$ and C are ( $- 2,2$ ), ( 1,3 ) and ( $3 , - 3$ ) respectively.\\
(i) Find the gradients of the lines AB and BC .\\
(ii) Show that the triangle ABC is a right-angled triangle.\\
(iii) Find the area of the triangle ABC .
\hfill \mbox{\textit{OCR MEI C1 Q4 [5]}}