Question 1: Find the midpoint of the line segment with endpoints A(2, 4) and B(6, 8).

Answer: Midpoint: (4, 6)

Question 2: Calculate the midpoint of points P(1, -3) and Q(5, 7).

Answer: Midpoint: (3, 2)

Question 3: Given points M(2, 5) and N(8, 11), verify if their midpoint is (5, 8).

Answer: Yes, midpoint is (5, 8)

Question 4: Plot the points A(1, 2) and B(7, 10). Draw the segment and locate its midpoint.

Answer: Midpoint: (4, 6)

Question 5: What is the midpoint of segment joining C(3, 7) and D(9, 3)?

Answer: Midpoint: (6, 5)

Question 6: Construct a triangle with vertices at (2, 3), (8, 3), and (5, 7). Find the midpoint of the base.

Answer: Midpoint of base: (5, 3)

Question 7: A line segment has endpoints at (4, 2) and (10, 14). Find its midpoint.

Answer: Midpoint: (7, 8)

Question 8: Two points are given as A(0, 0) and B(12, 8). If the midpoint is (6, 4), is this correct? Explain.

Answer: Yes, because midpoint formula: ((0+12)/2, (0+8)/2) = (6, 4)

Question 9: Given points P(5, 2) and Q(9, 10), find the midpoint and then verify whether this midpoint lies on the line y = 2x - 8.

Answer: Midpoint: (7, 6). Check: y=2(7)-8=14-8=6, matches y-coordinate, so yes.

Question 10: A construction: Draw points E(1, 4) and F(9, 12). Connect them and locate the midpoint. Then, find the midpoint of the segment joining the midpoints of two other segments E-G and F-H, where G(1, 8) and H(9, 16).

Answer: Midpoint of EF: (5, 8); Midpoint of EG: (1, 6); Midpoint of FH: (9, 12); Midpoint of these midpoints: (5, 9)

Question 11: Identify the common mistake: The midpoint between (3, 5) and (7, 9) is calculated as (5, 7). Correct this mistake and find the actual midpoint.

Answer: Correct midpoint: ( (3+7)/2, (5+9)/2 ) = (5, 7). The initial calculation was correct.