| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Perpendicular bisector of segment |
| Difficulty | Standard +0.3 This is a straightforward coordinate geometry question requiring standard techniques: finding the gradient of a perpendicular line, using the midpoint formula, and solving simultaneous equations. While it involves multiple steps, each step uses routine A-level methods with no novel insight required, making it slightly easier than average. |
| 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 | Marks | Guidance |
| Gradient \(= 1.5\), Gradient of perpendicular \(= -\frac{2}{3}\) | B1 | |
| Equation of \(AB\): \(y - 6 = -\frac{2}{3}(x + 2)\) or \(3y + 2x = 14\) oe | M1 A1 | Correct use of straight line equation with a changed gradient and \((-2, 6)\), the \((-(-2))\) must be resolved for the A1 ISW. Using \(y = mx + c\) gets A1 as soon as \(c\) is evaluated. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Simultaneous equations \(\rightarrow\) Midpoint \((1, 4)\) | M1 | Attempt at solution of simultaneous equations as far as \(x =\) or \(y =\) |
| Use of midpoint or vectors \(\rightarrow B(4, 2)\) | M1A1 | Any valid method leading to \(x\), or to \(y\). |
## Question 2:
**Part (i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Gradient $= 1.5$, Gradient of perpendicular $= -\frac{2}{3}$ | **B1** | |
| Equation of $AB$: $y - 6 = -\frac{2}{3}(x + 2)$ or $3y + 2x = 14$ oe | **M1 A1** | Correct use of straight line equation with a changed gradient and $(-2, 6)$, the $(-(-2))$ must be resolved for the **A1** ISW. Using $y = mx + c$ gets **A1** as soon as $c$ is evaluated. |
**Part (ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Simultaneous equations $\rightarrow$ Midpoint $(1, 4)$ | **M1** | Attempt at solution of simultaneous equations as far as $x =$ or $y =$ |
| Use of midpoint or vectors $\rightarrow B(4, 2)$ | **M1A1** | Any valid method leading to $x$, or to $y$. |
---2 The point $A$ has coordinates ( $- 2,6$ ). The equation of the perpendicular bisector of the line $A B$ is $2 y = 3 x + 5$.\\
(i) Find the equation of $A B$.\\
(ii) Find the coordinates of $B$.\\
\hfill \mbox{\textit{CAIE P1 2017 Q2 [6]}}