Variation 1 · answer guide

Vectors — Reflection from a projection

Question

The projection of onto a line through the origin is . The reflection of in that line is

This practice question was inspired by Question 9 in the 2020 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: write the vector relationship component by component, then use a dot product, magnitude or scalar multiple as required.Reflection .
Finish the calculation, then check that the result meets the question’s conditions.Midpoint check: .
Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: The midpoint of a point and its reflection is the projection foot.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.