Question 1: Construct the perpendicular bisector of the line segment joining points (2, 3) and (6, 7).

Answer: Perpendicular bisector drawn through midpoint, at right angles to segment

Question 2: Calculate the length of the line segment joining points (4, 5) and (8, 9).

Answer: 5.7

Question 3: Find the coordinates of the midpoint of the segment joining (1, 2) and (5, 6).

Answer: (3, 4)

Question 4: On the grid, draw the line segment between (3, 3) and (7, 7). Construct its perpendicular bisector.

Answer: Perpendicular bisector passing through (5, 5), at right angles to segment

Question 5: Given points A(2, 4) and B(8, 10), determine if the point (5, 7) lies on the perpendicular bisector of AB.

Answer: Yes

Question 6: Construct the perpendicular bisector of a segment of length 6 units on the grid. Label the midpoint and the bisector.

Answer: Bisector at midpoint, perpendicular at right angles to segment

Question 7: A triangle has sides of lengths 5 cm, 7 cm, and 8 cm. Construct the perpendicular bisectors of two sides and find the point of intersection.

Answer: Point of intersection is the circumcenter where all perpendicular bisectors meet

Question 8: Explain why the perpendicular bisector of a side of a triangle passes through the triangle's circumcenter.

Answer: Because it is equidistant from the endpoints of the side, and all such bisectors intersect at the point equidistant from all vertices

Question 9: Using the grid, construct the perpendicular bisector of the segment joining (1, 1) and (9, 5). Extend your bisector and identify the point where it intersects the line y=0.

Answer: Intersection at (5, 0)

Question 10: Identify a common mistake students make when constructing a perpendicular bisector and describe how to avoid it.

Answer: Incorrectly locating the midpoint or drawing at an angle other than 90°. To avoid, use a compass to find the midpoint and a ruler to draw a perfect perpendicular line.

Question 11: Verify the perpendicular bisector constructed in Question 1 by measuring the distances from the midpoint to each endpoint. What do you observe?

Answer: Distances are equal, confirming the bisector's correctness