Question 1: Find the coordinates of the midpoint of the segment joining points A(2, 4) and B(6, 10).

Answer: 4, 7

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

Answer: 2, 2

Question 3: Determine the midpoint of segment MN where M(1, −2) and N(5, 6).

Answer: 3, 2

Question 4: Construct a triangle with vertices at A(1, 2), B(5, 2), and C(3, 6). Find the midpoint of side AB.

Answer: 3, 2

Question 5: Find the midpoint of the segment joining the points (−4, 3) and (2, −5).

Answer: −1, −1

Question 6: A line segment has endpoints at (3, 7) and (9, 15). Show that the midpoint is at (6, 11).

Answer: Midpoint = ((3+9)/2, (7+15)/2) = (6, 11)

Question 7: Prove that the midpoint of a segment is equidistant from both endpoints using the coordinate geometry method.

Answer: Distance from midpoint to each endpoint is equal by calculating √[(x−x₁)² + (y−y₁)²]

Question 8: In triangle ABC, the points D and E are midpoints of sides AB and AC respectively. Prove that DE is parallel to BC and DE = ½ BC.

Answer: Use midpoints and vector properties to show DE is parallel to BC and length is half.

Question 9: Given points P(1, 2) and Q(5, 8), find the coordinates of the midpoint, then verify if the midpoint divides the segment into two equal parts.

Answer: Midpoint = (3, 5). Yes, it divides into two equal parts.

Question 10: A complex problem: Points R(−2, 3), S(4, 9), and T(1, 6). Find the midpoints of R–S and R–T and determine if these midpoints align collinearly.

Answer: Midpoints: M1(1, 6), M2(−0.5, 4.5). Check if points are collinear by slope method.