| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Parallel line through point |
| Difficulty | Easy -1.2 This is a routine C1 coordinate geometry question requiring two standard steps: find the gradient of AB using the gradient formula, then use y - y₁ = m(x - x₁) for the parallel line through C. The rearrangement to the required form is straightforward algebra. Below average difficulty as it's a direct application of basic techniques with no problem-solving required. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks | Guidance |
|---|---|---|
| \(\text{grad } AB = \frac{-2-0}{5-(-3)} = -\frac{1}{4}\) | M1 A1 | |
| \(\therefore y - 1 = -\frac{1}{4}(x - 4)\) | M1 | |
| \(4y - 4 = -x + 4\) | ||
| \(x + 4y = 8\) | A1 | (4) |
$\text{grad } AB = \frac{-2-0}{5-(-3)} = -\frac{1}{4}$ | M1 A1 |
$\therefore y - 1 = -\frac{1}{4}(x - 4)$ | M1 |
$4y - 4 = -x + 4$ | |
$x + 4y = 8$ | A1 | (4)\begin{enumerate}
\item The points $A , B$ and $C$ have coordinates $( - 3,0 ) , ( 5 , - 2 )$ and $( 4,1 )$ respectively.
\end{enumerate}
Find an equation for the straight line which passes through $C$ and is parallel to $A B$.\\
Give your answer in the form $a x + b y = c$, where $a$, $b$ and $c$ are integers.\\
\hfill \mbox{\textit{Edexcel C1 Q1 [4]}}