Vectors and Geometry — Interactive Lesson (Ages 14–16)

Can your students express BP in terms of a, b and c? This 16-slide interactive lesson uses vectors to solve geometry problems in shapes such as trapeziums and hexagons.

Mastering Vectors and Geometry at GCSE

Students learn to use vectors to solve problems in geometry and to describe the position of any point in two dimensions. Given vectors a and b in a diagram, they express other vectors such as AD = 3a, AL = 3a + 2b and KA = −2a − 2b. Problems include a trapezium where Q is the midpoint of CB and P divides CD in the ratio 1 : 3, a regular hexagon with centre O, and a parallelogram, each requiring vectors to be written in terms of a, b and sometimes c.

What’s Included

• 16-slide interactive lesson on vectors and geometry
• Learning objectives on using vectors to solve geometry problems
• Worked examples expressing vectors in terms of given vectors
• A trapezium problem with a midpoint and a ratio point
• A regular hexagon and a parallelogram problem, with instant feedback

Key Benefits for Students

• Builds fluency expressing one vector in terms of others
• Applies vectors to genuine geometry problems
• Uses midpoints and ratios within vector expressions
• Instant feedback on answer questions

Why Teachers Love It

• No prep — ready for whole-class teaching on an interactive whiteboard
• A concise lesson that fits a single session
• Self-marking questions support independent practice
• Suits higher-tier revision and homework
• Stretches confident vector students further

Love this? You’ll love…

• Introduction to Vectors — Interactive Lesson (Ages 14–16)
• Column Vectors — Interactive Lesson & Worksheet (Ages 14–16)
• Scalar Multiplications Of Vectors — Interactive Lesson (Year 10)

A dependable addition to a GCSE geometry topic, giving higher-tier students practice applying vectors to genuine proof-style problems. This is exactly the kind of question that separates the top grades.

Stretch confident vector skills — Add to Basket.

FAQs

What year group is this for?
Years 10–11 (ages 14–16), GCSE higher tier.

Does it use ratios within shapes?
Yes — for example a point dividing a line in a given ratio.

Is it self-marking?
Yes, with instant feedback on the questions.