O-LevelAdditional MathematicsVectors in two dimensions4037/22 · May/June 2021 · Q68 Marks
The points A(5, -4) and C(11, 6) are such that AC is the diagonal of a square, ABCD.
- (a)Find the length of the line AC.[2]
- (b)(i)The coordinates of the centre, E, of the square are (8, y). Find the value of y.[1]
- (b)(ii)Find the equation of the diagonal BD.[3]
- (b)(iii)Given that the x-coordinate of B is less than the x-coordinate of D, write EB and ED as column vectors.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- (a) M1 √(11-5)² + (6--4)² oe
- (a) A1 11.7 or 11.66[19...] rot to 4 or more figs
- (b)(i) B1 [y= ] 1
- (b)(ii) B1 m_AC = (6--4)/(11-5) or 10/6 nfww oe
- (b)(ii) M1 m_BD = -1 / (their 10/6) oe
- (b)(ii) A1 FT their 1 from (b)(i) and their perpendicular gradient y - their 1 = -3/5 (x-8) oe isw
- (b)(iii) B2 B1 for either (-5, 3) and (5, -3)
- (b)(iii) If 0 scored, SC1 for –5i + 3j and 5i -3j
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