A-LevelMathematicsCoordinate geometry9709/12 · May/June 2011 · Q77 Marks
The line L₁ passes through the points A (2, 5) and B (10, 9). The line L₂ is parallel to L₁ and passes through the origin. The point C lies on L₂ such that AC is perpendicular to L₂. Find
- (i)the coordinates of C,[5]
- (ii)the distance AC.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- [5] (i) (2, 5) to (10,9) gradient = ½; B1 co; Equation of L₂ y = ½x.; B1√ √ on gradient of L1; Gradient of perpendicular = -2; M1 Use of m₁m₂= -1; Eqn of Perp y − 5 = −2(x - 2); M1 Correct form of line eqn; A1 co; Sim Eqns → C(3.6, 1.8)
- [2] (ii) d² = 1.6² + 3.2² → d = 3.58; M1 Correct method for AC; A1 co (accept with √5 in answer)
Write your answer and get it marked
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.
Sign up free →