| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| 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 multi-part coordinate geometry question testing basic skills: finding line equations from point and gradient, solving simultaneous equations, finding midpoints, and verifying a line passes through a point. All parts use standard C1 techniques with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(y - 3 = \frac{3}{2}(x - 5)\) | M1 | |
| \(y = \frac{3}{2}x - \frac{9}{2}\) | A1 | |
| (b) \(3x - 4(\frac{1}{2}x - \frac{9}{2}) + 3 = 0\) | M1 | |
| \(x = 7\) | A1 | |
| \(\therefore B(7, 6)\) | A1 | |
| (c) \(= (\frac{5+7}{2}, \frac{3+6}{2}) = (6, \frac{9}{2})\) | M1 A1 | |
| (d) \(l_2: y = \frac{2}{3}x + \frac{3}{4} \therefore \text{grad} = \frac{3}{4}\) | B1 | |
| \(\therefore y - \frac{9}{2} = \frac{3}{4}(x - 6)\) | M1 | |
| \(y = \frac{3}{4}x\) | A1 | |
| when \(x = 0, y = 0 \therefore\) passes through origin | A1 | (11) |
**(a)** $y - 3 = \frac{3}{2}(x - 5)$ | M1 |
$y = \frac{3}{2}x - \frac{9}{2}$ | A1 |
**(b)** $3x - 4(\frac{1}{2}x - \frac{9}{2}) + 3 = 0$ | M1 |
$x = 7$ | A1 |
$\therefore B(7, 6)$ | A1 |
**(c)** $= (\frac{5+7}{2}, \frac{3+6}{2}) = (6, \frac{9}{2})$ | M1 A1 |
**(d)** $l_2: y = \frac{2}{3}x + \frac{3}{4} \therefore \text{grad} = \frac{3}{4}$ | B1 |
$\therefore y - \frac{9}{2} = \frac{3}{4}(x - 6)$ | M1 |
$y = \frac{3}{4}x$ | A1 |
when $x = 0, y = 0 \therefore$ passes through origin | A1 | (11)The straight line $l_1$ has gradient $\frac{3}{4}$ and passes through the point $A(5, 3)$.
\begin{enumerate}[label=(\alph*)]
\item Find an equation for $l_1$ in the form $y = mx + c$. [2]
\end{enumerate}
The straight line $l_2$ has the equation $3x - 4y + 3 = 0$ and intersects $l_1$ at the point $B$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the coordinates of $B$. [3]
\item Find the coordinates of the mid-point of $AB$. [2]
\item Show that the straight line parallel to $l_2$ which passes through the mid-point of $AB$ also passes through the origin. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q8 [11]}}