CAIE P1 2019 November — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStraight Lines & Coordinate Geometry
TypeParallel line through point
DifficultyEasy -1.2 This is a straightforward coordinate geometry question requiring only routine procedures: finding a midpoint using the standard formula, converting a line equation to gradient form to identify the slope, then using y - y₁ = m(x - x₁). All steps are standard AS-level techniques with no problem-solving or insight required, making it easier than average.
Spec1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships

2 The point \(M\) is the mid-point of the line joining the points \(( 3,7 )\) and \(( - 1,1 )\). Find the equation of the line through \(M\) which is parallel to the line \(\frac { x } { 3 } + \frac { y } { 2 } = 1\).

Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
Attempt to find the midpoint \(M\)M1
\((1, 4)\)A1
Use a gradient of \(\pm\frac{2}{3}\) and *their* \(M\) to find the equation of the lineM1
Equation is \(y - 4 = -\frac{2}{3}(x-1)\)A1 AEF
Alternative method for question 2:
AnswerMarks Guidance
AnswerMarks Guidance
Attempt to find the midpoint \(M\)M1
\((1, 4)\)A1
Replace 1 in the given equation by \(c\) and substitute *their* \(M\)M1
Equation is \(y - 4 = -\frac{2}{3}(x-1)\)A1 AEF
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempt to find the midpoint $M$ | M1 | |
| $(1, 4)$ | A1 | |
| Use a gradient of $\pm\frac{2}{3}$ and *their* $M$ to find the equation of the line | M1 | |
| Equation is $y - 4 = -\frac{2}{3}(x-1)$ | A1 | AEF |

**Alternative method for question 2:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempt to find the midpoint $M$ | M1 | |
| $(1, 4)$ | A1 | |
| Replace 1 in the given equation by $c$ and substitute *their* $M$ | M1 | |
| Equation is $y - 4 = -\frac{2}{3}(x-1)$ | A1 | AEF |

---
2 The point $M$ is the mid-point of the line joining the points $( 3,7 )$ and $( - 1,1 )$. Find the equation of the line through $M$ which is parallel to the line $\frac { x } { 3 } + \frac { y } { 2 } = 1$.\\

\hfill \mbox{\textit{CAIE P1 2019 Q2 [4]}}