WJEC Unit 1 2019 June — Question 04 15 marks

Exam BoardWJEC
ModuleUnit 1 (Unit 1)
Year2019
SessionJune
Marks15
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStraight Lines & Coordinate Geometry
TypeIntersection of two lines
DifficultyEasy -1.3 This is a routine coordinate geometry question testing standard techniques: finding line equations from two points, intersection points, perpendicularity, distance formula, and angle calculation using trigonometry. All parts follow textbook procedures with no problem-solving insight required. The 'show that' parts make it even more straightforward as students know the target answer.
Spec1.03a 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 \(A(-1, 3)\) and \(B(2, 9)\). The line \(L_2\) has equation \(2y + x = 25\) and intersects \(L_1\) at the point \(C\). \(L_2\) also intersects the \(x\)-axis at the point \(D\).
  1. Show that the equation of the line \(L_1\) is \(y = 2x + 5\). [3]
    1. Find the coordinates of the point \(D\).
    2. Show that \(L_1\) and \(L_2\) are perpendicular.
    3. Determine the coordinates of \(C\). [5]
  2. Find the length of \(CD\). [2]
  3. Calculate the angle \(ADB\). Give your answer in degrees, correct to one decimal place. [5]

The line $L_1$ passes through the points $A(-1, 3)$ and $B(2, 9)$. The line $L_2$ has equation $2y + x = 25$ and intersects $L_1$ at the point $C$. $L_2$ also intersects the $x$-axis at the point $D$.

\begin{enumerate}[label=(\alph*)]
\item Show that the equation of the line $L_1$ is $y = 2x + 5$. [3]

\item \begin{enumerate}[label=(\roman*)]
\item Find the coordinates of the point $D$.
\item Show that $L_1$ and $L_2$ are perpendicular.
\item Determine the coordinates of $C$. [5]
\end{enumerate}

\item Find the length of $CD$. [2]

\item Calculate the angle $ADB$. Give your answer in degrees, correct to one decimal place. [5]
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 1 2019 Q04 [15]}}