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CDEF is a quadrilateral - Edexcel - GCSE Maths - Question 24 - 2022 - Paper 3

Question 24

CDEF is a quadrilateral. $ ext{FE} = a ext{ and } ext{ED} = b ext{ and } ext{CD} = 2a$ The point P is such that $ ext{CEF}$ is a straight line and that $ ext{C... show full transcript

Worked Solution & Example Answer:CDEF is a quadrilateral - Edexcel - GCSE Maths - Question 24 - 2022 - Paper 3

Step 1

CE = EP

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Answer

Given that $ext{CE} = ext{EP}$ and $ext{FE} = a$ , we can represent the points in vector form.

Let $ext{C} = ext{O}$ (the origin). Thus,

$ext{E} = a ext{ in the direction of } ext{CE}$ ,
$ext{F} = ext{E} + a = a + a = 2a$ .

This allows us to express the vectors:

$ext{CF} = ext{F} - ext{C} = 2a - 0 = 2a$ ,
$ext{DP} = ext{P} - ext{D} = ext{E} + b - (2a) = 2a + b - 2a = b$ .

Step 2

CF and DP

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Answer

$ext{CF} = 2a$ and $ext{DP} = b$ . Using the fact that $ext{CF} ext{ and } ext{DP}$ are both directed along the same line, we conclude that the vectors are proportional. Hence, $ext{CF}$ is parallel to $ext{DP}$ .$

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