Points Dividing a Line in a Given Ratio
Part of Vectors (Geometry Proofs) — GCSE Mathematics
This deep dive covers Points Dividing a Line in a Given Ratio 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 8 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 8 of 11
Practice
14 questions
Recall
12 flashcards
Points Dividing a Line in a Given Ratio
If point P divides line segment AB in the ratio m:n, then:
OP = OA + [m ÷ (m + n)] × AB
This means P is m/(m+n) of the way from A to B.
Worked Example: OA = a, OB = b. Point P divides AB in ratio 2:1. Find OP.
Step 1: AB = OB - OA = b - a
Step 2: P is 2/3 of the way from A to B: AP = ⅔AB = ⅔(b - a)
Step 3: OP = OA + AP = a + ⅔(b - a) = a + ⅔b - ⅔a = ⅓a + ⅔b