OCR MEI C1 — Question 8 3 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStraight Lines & Coordinate Geometry
TypePerpendicular line through point
DifficultyModerate -0.8 This is a straightforward coordinate geometry question requiring two standard techniques: finding the gradient of the given line (rearranging to y = mx + c form or using -A/B), then using the perpendicular gradient rule (negative reciprocal) and point-slope form. It's routine practice with no problem-solving required, making it easier than average but not trivial since it involves multiple steps.
Spec1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships
8 Find the equation of the line that passes through the point \(( 1,2 )\) and is perpendicular to the line \(3 x + 2 y = 5\).
Question 8:
AnswerMarks Guidance
Gradient of \(3x + 2y = 5\) is \(\frac{-3}{2}\)B1
\(\Rightarrow\) Gradient of perpendicular line \(= \frac{2}{3}\)M1
\(\Rightarrow y - 2 = \frac{2}{3}(x-1) \Rightarrow 3y - 6 = 2x - 2\)A1 Accept other forms
\(\Rightarrow 3y = 2x + 4\) Total: 3 
# Question 8:
Gradient of $3x + 2y = 5$ is $\frac{-3}{2}$ | B1 |
$\Rightarrow$ Gradient of perpendicular line $= \frac{2}{3}$ | M1 |
$\Rightarrow y - 2 = \frac{2}{3}(x-1) \Rightarrow 3y - 6 = 2x - 2$ | A1 | Accept other forms
$\Rightarrow 3y = 2x + 4$ | | **Total: 3**

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8 Find the equation of the line that passes through the point $( 1,2 )$ and is perpendicular to the line $3 x + 2 y = 5$.

\hfill \mbox{\textit{OCR MEI C1  Q8 [3]}}
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