1. 1
   A drone delivery service marks warehouse locations using coordinates.

   (a)

   A drone delivery service marks warehouse locations as coordinates. Warehouse $A$ is at $(1, 2)$ and Warehouse $B$ is at $(7, 10)$. Find the distance $AB$.

   [1 mark]

   • A100
   • B14
   • C8
   • D10

   (b)

   Find the midpoint of the line segment $AB$, where $A = (1,2)$ and $B = (7,10)$.

   [1 mark]

   • A$(8, 12)$
   • B$(3, 4)$
   • C$(4, 6)$
   • D$(6, 4)$

   (c)

   A charging station is placed at the midpoint of $AB$, which is $(4,6)$. Find the distance from Warehouse $A = (1,2)$ to the charging station.

   [1 mark]

   • A7
   • B5
   • C6
   • D10

   Total for question 1: 3 marks

2. 2
   A surveyor records boundary posts of a field using coordinates to calculate distances and midpoints.

   (a)

   A surveyor records two boundary posts of a field at points $P = (-3, 4)$ and $Q = (5, -2)$. Calculate the length of the boundary $PQ$, showing full working.

   [2 marks]

   (b)

   Find the coordinates of the midpoint of $PQ$, where $P = (-3, 4)$ and $Q = (5, -2)$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A ship's radar tracks two vessels and a rescue point using coordinate geometry.

   (a)

   A ship's radar plots two vessels at $R = (2, 8)$ and $S = (10, 3)$. Calculate the distance between the vessels, giving your answer to 1 decimal place.

   [3 marks]

   (b)

   A rescue boat is stationed at the midpoint of $RS$, where $R = (2,8)$ and $S = (10,3)$. Find the coordinates of the rescue boat's position, then calculate the distance from the rescue boat to vessel $R$, giving your answer to 1 decimal place.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A city planner designs a triangular park using three coordinate points and needs to check its properties.

   (a)

   A city planner marks three park entrances at $A = (0, 0)$, $B = (6, 8)$, and $C = (12, 0)$. Calculate the lengths of all three sides of the triangle formed by these points, showing full working for each.

   [4 marks]

   (b)

   Using the side lengths found in part (a) ($AB=10$, $BC=10$, $AC=12$), state what type of triangle $ABC$ is, giving a geometric reason.

   [4 marks]

   (c)

   The planner wants to place a fountain at the midpoint of $AC$, where $A=(0,0)$ and $C=(12,0)$, and connect it to entrance $B=(6,8)$ with a path. Find the coordinates of the fountain, calculate the length of the path from the fountain to $B$, and explain what this length represents in relation to triangle $ABC$.

   [5 marks]

   Total for question 4: 13 marks

End of questions