2020 HSC Mathematics Extension 1
Question 9:
Vectors
The projection of the vector onto the line is .
The point is reflected in the line to a point .
What is the position vector of the point ?
How to recognise this question
Question type: vectors
- The command and notation point to vectors.
- The requested response is a multiple choice.
How to handle it: write the vector relationship component by component, then use a dot product, magnitude or scalar multiple as required.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- If is a point vector and , the reflection is .
- Here and .
- So .
- Geometrically, is the midpoint of and : .
- Answer: B.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
The projection of onto a line through the origin is . The reflection of in that line is
Question 2
Projection of onto the -axis is . The reflection of in the -axis is
Question 3
Projection of onto is . The reflected point is