| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Intersection of two lines |
| Difficulty | Moderate -0.8 This is a straightforward C1 coordinate geometry question requiring standard techniques: using y - y₁ = m(x - x₁) to find line equations, recognizing perpendicular gradients (m₁ × m₂ = -1), and solving simultaneous linear equations. All steps are routine textbook exercises with no problem-solving insight required, making it easier than average but not trivial due to the multi-part structure. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| (a) \(y + 5 = 2(x-4)\) → \(y = 2x - 13\) | M1 A1 | |
| (b) \(3x - y = 4 \Rightarrow y = 3x - 4\), grad \(= 3\); grad \(l_2 = \frac{-1}{3} = -\frac{1}{3}\) | M1 A1 | |
| \(\therefore y - 0 = -\frac{1}{3}(x-3)\) \(\left[y = -\frac{1}{3}x + 1\right]\) | A1 | |
| (c) \(2x - 13 = -\frac{1}{3}x + 1\) → \(x = 6\) | M1 A1 | |
| \(\therefore (6, -1)\) | A1 | (8) |
## Question 7:
| Answer/Working | Marks | Notes |
|---|---|---|
| **(a)** $y + 5 = 2(x-4)$ → $y = 2x - 13$ | M1 A1 | |
| **(b)** $3x - y = 4 \Rightarrow y = 3x - 4$, grad $= 3$; grad $l_2 = \frac{-1}{3} = -\frac{1}{3}$ | M1 A1 | |
| $\therefore y - 0 = -\frac{1}{3}(x-3)$ $\left[y = -\frac{1}{3}x + 1\right]$ | A1 | |
| **(c)** $2x - 13 = -\frac{1}{3}x + 1$ → $x = 6$ | M1 A1 | |
| $\therefore (6, -1)$ | A1 | **(8)** |
---7. The straight line $l _ { 1 }$ has gradient 2 and passes through the point with coordinates $( 4 , - 5 )$.
\begin{enumerate}[label=(\alph*)]
\item Find an equation for $l _ { 1 }$ in the form $y = m x + c$.
The straight line $l _ { 2 }$ is perpendicular to the line with equation $3 x - y = 4$ and passes through the point with coordinates $( 3,0 )$.
\item Find an equation for $l _ { 2 }$.
\item Find the coordinates of the point where $l _ { 1 }$ and $l _ { 2 }$ intersect.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [8]}}