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

Answer: 5

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

Answer: 10

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

Answer: 6.4

Question 4: Construct a right-angled triangle on the grid with legs of 5 units and 12 units. What is the length of the hypotenuse?

Answer: 13

Question 5: Plot the points (1, 2) and (4, 6). Then, calculate the distance between them.

Answer: 5

Question 6: A ladder is leaning against a wall. The base of the ladder is 3 meters from the wall, and the top reaches 4 meters high. How long is the ladder?

Answer: 5

Question 7: A drone flies from point A (2, 3) to point B (8, 7). Calculate the straight-line distance.

Answer: 7.2

Question 8: In a right triangle with hypotenuse 15 units, one leg is 9 units long. Find the length of the other leg.

Answer: 12

Question 9: A surveyor measures two points with coordinates (x1, y1) and (x2, y2). The distance between them is 13 units. If x1=5, y1=12, find x2 and y2 assuming they are aligned horizontally.

Answer: x2=5, y2=25 or x2=5, y2=-1

Question 10: Identify and correct the mistake in calculating the distance between points (1, 2) and (4, 6) if a student used 3^2 + 4^2 instead of the correct 3^2 + 4^2.

Answer: The correct differences are (3, 4), so the distance is 5. The student’s calculation was correct.

Question 11: Challenge: A triangle has sides of 7, 24, and a hypotenuse. Is it a right triangle? Justify your answer.

Answer: Yes, because 7^2 + 24^2 = 49 + 576 = 625, which equals 25^2, so the hypotenuse is 25.