Worked Example: Midpoint Vector
Part of Vectors (Geometry Proofs) — GCSE Mathematics
This deep dive covers Worked Example: Midpoint Vector within Vectors (Geometry Proofs) for GCSE Mathematics. Revise Vectors (Geometry Proofs) in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 11
Practice
14 questions
Recall
12 flashcards
Worked Example: Midpoint Vector
O is the origin. OA = a, OB = b. M is the midpoint of AB. Find OM.
Step 1: Find AB. AB = AO + OB = -a + b
Step 2: M is the midpoint, so AM = ½AB = ½(-a + b)
Step 3: OM = OA + AM = a + ½(-a + b) = a - ½a + ½b = ½a + ½b
Answer: OM = ½(a + b) — the average of the two position vectors.