1. 1
   A drone delivery company plots delivery points on a coordinate grid, with the depot at the origin O(0, 0). Point A has coordinates (4, 3) and point B has coordinates (-2, 5).

   (a)

   In which quadrant does point B lie?

   [1 mark]

   • AFirst quadrant
   • BFourth quadrant
   • CThird quadrant
   • DSecond quadrant

   (b)

   What are the coordinates of the midpoint of the line segment AB?

   [1 mark]

   • A(1, 4)
   • B(2, 8)
   • C(1, 1)
   • D(6, -2)

   (c)

   What is the gradient of the line OA, where O is the origin (0, 0)?

   [1 mark]

   • A$\frac{4}{3}$
   • B$3$
   • C$\frac{3}{4}$
   • D$-\frac{3}{4}$

   Total for question 1: 3 marks

2. 2
   A straight line conversion graph converts distances measured in miles (x) to kilometres (y). The line passes through the points (0, 0) and (5, 8).

   (a)

   Find the gradient of the conversion line, and state clearly what this gradient represents in the context of the graph.

   [2 marks]

   (b)

   A cyclist travels 12.5 miles. Using the gradient found above, calculate the equivalent distance in kilometres.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Line segment PQ has endpoints P(-3, 1) and Q(5, 7).

   (a)

   Find the coordinates of the midpoint M of PQ, showing your method.

   [3 marks]

   (b)

   Find the equation, in the form $y = mx + c$, of the straight line that passes through M (the midpoint of PQ found above) and is parallel to PQ.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   ABCD is a parallelogram with vertices A(-4, -1), B(2, 3) and D(-6, 5).

   (a)

   Using the fact that the diagonals of a parallelogram bisect each other, find the coordinates of vertex C.

   [4 marks]

   (b)

   Using your coordinates for A and C, calculate the coordinates of M, the midpoint of diagonal AC, and confirm this matches the midpoint of BD.

   [4 marks]

   (c)

   Find the equation of the diagonal line AC in the form $y = mx + c$.

   [5 marks]

   Total for question 4: 13 marks

End of questions