A-LevelMathematicsCoordinate geometry9709/12 · May/June 2013 · Q77 Marks

The point R is the reflection of the point (−1, 3) in the line 3y + 2x = 33. Find by calculation the coordinates of R.

Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

[1] B1 Gradient of the line 3y + 2x = 33 is -2/3
[1] M1 Uses m1m2 = -1 to find the gradient of the perpendicular line (gradient = 3/2)
[1] M1 Correctly forms the equation of the perpendicular line passing through (-1, 3) (e.g., y - 3 = 3/2 (x + 1))
[1] M1 Solves the simultaneous equations of the given line and the perpendicular line to find the midpoint
[1] A1 Correct coordinates of the midpoint (3, 9)
[1] M1 Uses the midpoint formula or vector method to find the coordinates of R (e.g., (x_R + x_P)/2 = x_M)
[1] A1 Correct coordinates of R (7, 15)

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Coordinate geometry, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, May/June 2013 Paper 1 Variant 2, question 7.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content