Edexcel C1 — Question 27 10 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks10
PaperDownload PDF ↗
TopicStraight Lines & Coordinate Geometry
TypeIntersection of two lines
DifficultyModerate -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.
Spec1.03a Straight lines: equation forms y=mx+c, ax+by+c=0

The points \(A\) and \(B\) have coordinates \((4, 6)\) and \((12, 2)\) respectively. The straight line \(l_1\) passes through \(A\) and \(B\).
  1. 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 \(-4\).
  1. Write down an equation for \(l_2\). [1]
The lines \(l_1\) and \(l_2\) intercept at the point \(C\).
  1. Find the exact coordinates of the mid-point of \(AC\). [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 $ax + by = c$, 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  Q27 [10]}}