A-LevelMathematicsCoordinate geometry9709/12 · Oct/Nov 2010 · Q87 Marks
The diagram shows part of the curve y = 2/(1-x) and the line y = 3x + 4. The curve and the line meet at points A and B. [Figure 8.1]
- (i)Find the coordinates of A and B.[4]
- (ii)Find the length of the line AB and the coordinates of the mid-point of AB.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.
- [M1A1] 3x²+x−2=0 Eliminates x or y. Sets quadratic to 0.
- [M1] (x+1)(3x-2) → x = −1 or 2/3 Attempt to solve their equation
- [A1] (−1, 1), (2/3, 6) co
- [M1] AB² = (5/3)² + 5² √ their coordinates from (i)
- [A1] AB = 5.27(0...) Or (5√10)/3 oe
- [B1√] mid-point = (-1/6, 7/2) ft from their (i)
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