| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle through three points using perpendicular bisectors |
| Difficulty | Moderate -0.3 This is a structured multi-part coordinate geometry question with standard techniques throughout. Part (a) requires finding a line equation from two points (routine), part (b) uses perpendicular gradients and solving a linear equation, part (c) is straightforward area calculation, and part (d) involves finding a circle equation through three points using either simultaneous equations or recognizing the right angle property. While part (d) requires more steps, all techniques are standard AS-level material with no novel insights needed, making it slightly easier than average overall. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
The point $A$ has coordinates $(-2, 5)$ and the point $B$ has coordinates $(3, 8)$. The point $C$ lies on the $x$-axis such that $AC$ is perpendicular to $AB$.
\begin{enumerate}[label=(\alph*)]
\item Find the equation of $AB$. [3]
\item Show that $C$ has coordinates $(1, 0)$. [3]
\item Calculate the area of triangle $ABC$. [4]
\item Find the equation of the circle which passes through the points $A$, $B$ and $C$. [5]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2023 Q3 [15]}}