| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Rectangle or parallelogram vertices |
| Difficulty | Moderate -0.5 This is a straightforward coordinate geometry problem requiring perpendicular gradients, point-slope form, and basic vector/distance work. While it involves multiple steps (finding perpendicular gradient, equation of BC, intersection with x-axis, then locating D), each step uses standard techniques with no novel insight required. Slightly easier than average due to being a routine multi-part question with clear structure. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| m of \(AB = 1.5\) (or \(1\frac{1}{2}\)) | B1 | co anywhere |
| m of \(BC = -1 \div (\text{m of } AB) = -\frac{2}{3}\) | M1 | Use of \(m_1 m_2 = -1\) |
| \(\rightarrow\) Eqn \(y - 8 = -\frac{2}{3}(x+2)\) or \(3y + 2x = 20\) | M1, A1\(\sqrt{}\) [4] | Correct form – or \(y = mx + c\); co; (\(\sqrt{}\) needs both M marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Put \(y = 0 \rightarrow C(10, 0)\) | B1\(\sqrt{}\) | \(\sqrt{}\) in his linear equation |
| Vector move \(\rightarrow D(14, 6)\) | M1A1 [3] | completely correct method; co |
| (or sim eqns \(3y + 2x = 46\) and \(2y = 3x - 30\)) |
## Question 6(i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| m of $AB = 1.5$ (or $1\frac{1}{2}$) | B1 | co anywhere |
| m of $BC = -1 \div (\text{m of } AB) = -\frac{2}{3}$ | M1 | Use of $m_1 m_2 = -1$ |
| $\rightarrow$ Eqn $y - 8 = -\frac{2}{3}(x+2)$ or $3y + 2x = 20$ | M1, A1$\sqrt{}$ [4] | Correct form – or $y = mx + c$; co; ($\sqrt{}$ needs both M marks) |
## Question 6(ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Put $y = 0 \rightarrow C(10, 0)$ | B1$\sqrt{}$ | $\sqrt{}$ in his linear equation |
| Vector move $\rightarrow D(14, 6)$ | M1A1 [3] | completely correct method; co |
| (or sim eqns $3y + 2x = 46$ and $2y = 3x - 30$) | | |
---6\\
\includegraphics[max width=\textwidth, alt={}, center]{b24ed4c7-ab07-45f4-adf2-027734c36b62-3_593_878_269_635}
The diagram shows a rectangle $A B C D$. The point $A$ is $( 2,14 ) , B$ is $( - 2,8 )$ and $C$ lies on the $x$-axis. Find\\
(i) the equation of $B C$,\\
(ii) the coordinates of $C$ and $D$.
\hfill \mbox{\textit{CAIE P1 2007 Q6 [7]}}