Question 6 — IGCSE 0580 May/June 2023 Paper 41
Cambridge IGCSE Mathematics 0580, Extended tier, calculator. Topic: Co-ordinate geometry · Cartesian coordinates (2D). Worth 14 marks.
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Question text
6 (a) In the square ABCD, A has coordinates (-2, 1) and B has coordinates (1, 5).
C has coordinates (a, b), where a and b are both positive integers.
Find the coordinates of C and the coordinates of D.
You may use the grid to help you.
y
6
5
4
3
2
1
– 3 – 2 – 1 0 1 2 3 4 5 6 x
– 1
– 2
– 3
C ( ...................... , ...................... )
D ( ...................... , ...................... ) [4]
© UCLES 2023 0580/41/M/J/23
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(b) P has coordinates (-1, 3) and Q has coordinates (6, 4).
(i) Find the coordinates of the midpoint of PQ.
( ...................... , ...................... ) [2]
(ii) Find the length PQ.
................................................. [3]
(iii) Find the gradient of PQ.
................................................. [2]
(iv) Find the equation of the line parallel to PQ that crosses the x-axis at x = 2.
................................................. [3]
© UCLES 2023 0580/41/M/J/23 [Turn over
14
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