Question 1: Calculate the distance between the points (3, 4) and (7, 1).

Answer: 5

Question 2: Find the length of the hypotenuse of a right-angled triangle with legs measuring 6 units and 8 units.

Answer: 10

Question 3: Determine the distance between points (-2, 5) and (4, 1).

Answer: 6.4

Question 4: Plot the points (2, 3) and (5, 7). Using the grid, draw the line segment connecting them and find its length.

Answer: Approximately 4.24

Question 5: A ladder is leaning against a wall, reaching 9 meters high. The base of the ladder is 12 meters from the wall. Calculate the length of the ladder.

Answer: 15

Question 6: Two points, A (1, 2) and B (4, 6), are plotted on the grid. Without measuring, estimate the distance and then verify by calculation.

Answer: 5

Question 7: Construct a right-angled triangle on the grid with legs measuring 9 units and 12 units. Draw the hypotenuse and find its length.

Answer: 15

Question 8: A drone flies from point (2, 3) to point (8, 14). Calculate the straight-line distance between the two points.

Answer: 13

Question 9: Explain how the Pythagoras theorem can be used to determine the shortest path between two points on a grid when obstacles are present.

Answer: Students should describe using right triangles to find alternative routes that avoid obstacles by calculating direct distances versus detours.

Question 10: A school field is rectangular, measuring 40 meters by 30 meters. A drone is flying from one corner to the opposite corner. Calculate the flying distance.

Answer: 50

Question 11: Identify and correct the mistake in the following calculation: The distance between (1, 2) and (4, 6) is calculated as √(3² + 4²) = 7.

Answer: Incorrect; √(3² + 4²) = 5, not 7.