| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Perpendicular line through point |
| Difficulty | Moderate -0.8 This is a standard C1 coordinate geometry question testing perpendicular gradients (m₁ × m₂ = -1), finding line equations, solving simultaneous equations, and calculating triangle area. All techniques are routine textbook exercises with clear signposting across three parts, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| 8. continued | Leave blank |
| Answer | Marks | Guidance |
|---|---|---|
| Gradient of \(l_2\) is \(-\frac{1}{3}\) | B1 | |
| \(y - 2 = -\frac{1}{3}(x-6)\) \(\Rightarrow\) \(y = -\frac{1}{3}x + 4\) | M1 A1 ft | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(-\frac{1}{3}x + 4 = 3x - 6\) \(\Rightarrow\) \(x = 3\) | M1 A1 | |
| \(y = 3\) | A1 ft | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(y=0\); \(l_1: x=2\), \(l_2: x=12\) | B1 B1 ft | |
| \((2,0),\ (12,0),\ (3,3)\) — Area of triangle \(= \frac{1}{2}(10 \times 3) = 15\) | M1 A1 | 4 marks |
## Question 8:
### Part (a):
Gradient of $l_2$ is $-\frac{1}{3}$ | B1 |
$y - 2 = -\frac{1}{3}(x-6)$ $\Rightarrow$ $y = -\frac{1}{3}x + 4$ | M1 A1 ft | **3 marks**
### Part (b):
$-\frac{1}{3}x + 4 = 3x - 6$ $\Rightarrow$ $x = 3$ | M1 A1 |
$y = 3$ | A1 ft | **3 marks**
### Part (c):
$y=0$; $l_1: x=2$, $l_2: x=12$ | B1 B1 ft |
$(2,0),\ (12,0),\ (3,3)$ — Area of triangle $= \frac{1}{2}(10 \times 3) = 15$ | M1 A1 | **4 marks**
**Total: 10 marks**
---8. The straight line $l _ { 1 }$ has equation $y = 3 x - 6$. \\
The straight line $l _ { 2 }$ is perpendicular to $l _ { 1 }$ and passes through the point (6, 2).
\begin{enumerate}[label=(\alph*)]
\item Find an equation for $l _ { 2 }$ in the form $y = m x + c$, where $m$ and $c$ are constants. \\
(3) \\
The lines $l _ { 1 }$ and $l _ { 2 }$ intersect at the point $C$.
\item Use algebra to find the coordinates of $C$. \\
(3) \\
The lines $l _ { 1 }$ and $l _ { 2 }$ cross the $x$-axis at the points $A$ and $B$ respectively.
\item Calculate the exact area of triangle $A B C$. \\
(4) $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ $\_\_\_\_$ \\
\end{tabular} & Leave blank \\
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8. continued & Leave blank \\
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& \\
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\hfill \mbox{\textit{Edexcel C1 Q8 [10]}}