Year 12 Maths Extension 2 (2027)
Vectors
Vector Proofs in Geometry
ACCOUNT REQUIRED
Unlock all 20 questions & worked solutions
You're viewing a free preview. Create an account to access the complete question set, step-by-step solutions, and progress tracking.
All Questions
Access the full question set for every topic.
Worked Solutions
Step-by-step explanations for every answer.
Track Progress
Mark questions right or wrong and monitor your growth.
It's Free
No credit card required - sign up in under a minute.
Questions
Question 1
183502
In the parallelogram \(ABCD\) shown, prove using vectors that the diagonals bisect each other.
In parallelogram \(ABCD\), \(\overrightarrow{AB} = \overrightarrow{DC}\) gives \(\mathbf{a}+\mathbf{c} = \mathbf{b}+\mathbf{d}\), so the midpoints of \(AC\) and \(BD\) are both \(\dfrac{\mathbf{a}+\mathbf{c}}{2} = \dfrac{\mathbf{b}+\mathbf{d}}{2}\). The diagonals bisect each other.
📚 Want More Questions?
There are 19 more questions available. Create your free account to access the complete question set with detailed solutions.