| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Equation of line through two points |
| Difficulty | Moderate -0.8 This is a straightforward C1 coordinate geometry question requiring standard techniques: finding gradient from two points, writing line equations, 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-part nature. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
The points $A$ and $B$ have coordinates $(4, 6)$ and $(12, 2)$ respectively. The straight line $l_1$ passes through $A$ and $B$.
(a) Find an equation for $l_1$ in the form $ax + by = c$, where $a$, $b$ and $c$ are integers.
(4)
The straight line $l_2$ passes through the origin and has gradient $-4$.
(b) Write down an equation for $l_2$.
(1)
The lines $l_1$ and $l_2$ intersect at the point $C$.
(c) Find the exact coordinates of the mid-point of $AC$.
(5)5. 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 $a x + b y = c$, where $a$, b and $c$ are integers.
The straight line $l _ { 2 }$ passes through the origin and has gradient - 4 .
\item Write down an equation for $l _ { 2 }$.
The lines $l _ { 1 }$ and $l _ { 2 }$ intercept at the point $C$.
\item Find the exact coordinates of the mid-point of $A C$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q5 [10]}}