| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2019 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Intersection of two lines |
| Difficulty | Easy -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. |
| Spec | 1.03a 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 $D$.
\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]}}