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DEF is a triangle - Edexcel - GCSE Maths - Question 22 - 2020 - Paper 1

Question 22

DEF is a triangle. P is the midpoint of FD. Q is the midpoint of DE. → FD = a and FE = b Use a vector method to prove that PQ is parallel to FE.

Worked Solution & Example Answer:DEF is a triangle - Edexcel - GCSE Maths - Question 22 - 2020 - Paper 1

Step 1

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Answer

Since P and Q are midpoints, we can write:

$ext{PQ} = rac{1}{2} ext{FD} + rac{1}{2} ext{DE}$

Step 2

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Answer

We can express the vectors as:

$ext{PQ} = rac{1}{2} (a + b)$

Step 3

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Answer

Notice that:

$ext{FE} = b$

Thus:

$ext{PQ} = rac{1}{2}(a + b)$

This indicates that PQ is a linear combination of the vector b.

Step 4

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120 rated

Answer

Since PQ can be expressed as a scalar multiple of the vector b, we can conclude that:

$ext{PQ} ext{ is parallel to } FE.$

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