WJEC Unit 1 2022 June — Question 3 11 marks

Exam BoardWJEC
ModuleUnit 1 (Unit 1)
Year2022
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStraight Lines & Coordinate Geometry
TypeIntersection of two lines
DifficultyModerate -0.8 This is a straightforward coordinate geometry question testing standard techniques: finding line equations from two points, perpendicular gradients, intersection points, and triangle areas. All parts follow routine procedures with no problem-solving insight required. The multi-part structure (11 marks total) adds length but not conceptual difficulty—each step is a textbook exercise that AS-level students practice extensively.
Spec1.02q Use intersection points: of graphs to solve equations1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships

The line \(L_1\) passes through the points \(A(0, 5)\) and \(B(3, -1)\).
  1. Find the equation of the line \(L_1\). [3]
The line \(L_2\) is perpendicular to \(L_1\) and passes through the origin \(O\).
  1. Write down the equation of \(L_2\). [1]
The lines \(L_1\) and \(L_2\) intersect at the point \(C\).
  1. Calculate the area of triangle \(OAC\). [4]
  2. Find the equation of the line \(L_3\) which is parallel to \(L_1\) and passes through the point \(D(4, 2)\). [2]
  3. The line \(L_3\) intersects the \(y\)-axis at the point \(E\). Find the area of triangle \(ODE\). [1]

The line $L_1$ passes through the points $A(0, 5)$ and $B(3, -1)$.

\begin{enumerate}[label=(\alph*)]
\item Find the equation of the line $L_1$. [3]
\end{enumerate}

The line $L_2$ is perpendicular to $L_1$ and passes through the origin $O$.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Write down the equation of $L_2$. [1]
\end{enumerate}

The lines $L_1$ and $L_2$ intersect at the point $C$.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate the area of triangle $OAC$. [4]
\item Find the equation of the line $L_3$ which is parallel to $L_1$ and passes through the point $D(4, 2)$. [2]
\item The line $L_3$ intersects the $y$-axis at the point $E$. Find the area of triangle $ODE$. [1]
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 1 2022 Q3 [11]}}