| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Intersection of two lines |
| Difficulty | Moderate -0.8 This is a straightforward C1 coordinate geometry question requiring standard techniques: finding gradient and equation of a line through two points, writing equation of a line through origin, solving simultaneous equations, and finding a midpoint. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step nature and 10 total marks. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks |
|---|---|
| \(m = \frac{2-6}{12-4} = \left(-\frac{1}{2}\right)\) | M1 A1 |
| \(y - 6 = (m)(x-4)\) → \(x + 2y = 16\) | M1 A1 (4) |
| Answer | Marks |
|---|---|
| \(y = -4x\) | B1 (1) |
| Answer | Marks |
|---|---|
| \(x + 2(-4x) = 16\) → \(-7x = 16\) → \(x = -\frac{16}{7}\) | M1 A1 |
| \(y = \frac{64}{7}\) | A1 ft |
| \(A(4,6)\), \(C\left(-\frac{16}{7}, \frac{64}{7}\right)\); \(\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \to \left(\frac{6}{7}, \frac{53}{7}\right)\) | M1 A1 ft (5) |
## Part (a)
$m = \frac{2-6}{12-4} = \left(-\frac{1}{2}\right)$ | M1 A1
$y - 6 = (m)(x-4)$ → $x + 2y = 16$ | M1 A1 (4)
## Part (b)
$y = -4x$ | B1 (1)
## Part (c)
$x + 2(-4x) = 16$ → $-7x = 16$ → $x = -\frac{16}{7}$ | M1 A1
$y = \frac{64}{7}$ | A1 ft
$A(4,6)$, $C\left(-\frac{16}{7}, \frac{64}{7}\right)$; $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \to \left(\frac{6}{7}, \frac{53}{7}\right)$ | M1 A1 ft (5)
**Total: 10 marks**
---The points $A$ and $B$ have coordinates $(4, 6)$ and $(12, 2)$ respectively. The straight line $l_1$ passes through $A$ and $B$.
\begin{enumerate}[label=(\alph*)]
\item Find an equation for $l_1$ in the form $ax + by = c$, where $a$, $b$ and $c$ are integers. [4]
\end{enumerate}
The straight line $l_2$ passes through the origin and has gradient $-4$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Write down an equation for $l_2$. [1]
\end{enumerate}
The lines $l_1$ and $l_2$ intercept at the point $C$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the exact coordinates of the mid-point of $AC$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q8 [10]}}