| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Coordinates from geometric constraints |
| Difficulty | Moderate -0.8 This is a straightforward multi-part coordinate geometry question testing standard techniques: gradient calculation, perpendicular gradients (m₁ × m₂ = -1), distance formula, triangle area, and line equations. All parts follow routine procedures with no problem-solving insight required, making it easier than average but not trivial due to the multiple steps involved. |
| 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 |
The points $A(-1, -2)$, $B(7, 2)$ and $C(k, 4)$, where $k$ is a constant, are the vertices of $\triangle ABC$. Angle $ABC$ is a right angle.
\begin{enumerate}[label=(\alph*)]
\item Find the gradient of $AB$. [2]
\item Calculate the value of $k$. [2]
\item Show that the length of $AB$ may be written in the form $p\sqrt{5}$, where $p$ is an integer to be found. [3]
\item Find the exact value of the area of $\triangle ABC$. [3]
\item Find an equation for the straight line $l$ passing through $B$ and $C$. Give your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q8 [12]}}