Coordinate geometry — Negative direction vector

Question

Find the Cartesian form of , .

This practice question was inspired by Question 11(a) in the 2023 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: convert between parametric and Cartesian forms carefully, noting the direction of the parameter. from .
Finish the calculation, then check that the result meets the question’s conditions.Alternatively from .
State the final answer clearly in the form the question requested.Equate: .

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

Verification: Point at is : checks.

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