Question 1: Using a compass, construct the perpendicular bisector of a given line segment AB of length 6 cm. Label your bisector.

Answer: Perpendicular bisector constructed and labeled

Question 2: Construct a triangle with sides 5 cm, 7 cm, and 8 cm. Then, draw the perpendicular bisector of the longest side. Describe the steps you used.

Answer: Step-by-step construction with explanation

Question 3: Construct the perpendicular bisector of a segment AB that is 4 cm long, and find the point equidistant from A and B on the bisector.

Answer: Intersection point of bisector and distance points

Question 4: Plot the graph of y=2x and construct a perpendicular bisector of the segment connecting points (1,2) and (5,6).

Answer: Perpendicular bisector line drawn correctly

Question 5: Construct the perpendicular bisector of a 6 cm segment and identify the point that is equidistant from both endpoints. Provide the construction steps.

Answer: Detailed construction steps and identification of midpoint

Question 6: Construct a perpendicular bisector of a segment and explain how it can be used to find the center of a circle passing through the segment's endpoints.

Answer: Explanation of circle center construction via bisector

Question 7: Construct a segment of 7 cm and then draw its perpendicular bisector. Mark the point where the bisector intersects the segment and explain how this point relates to the segment.

Answer: Midpoint; equidistant from endpoints

Question 8: Construct a perpendicular bisector of a segment and then verify that any point on the bisector is equidistant from the segment's endpoints. Describe your verification process.

Answer: Verification using compass and measurement

Question 9: Given a segment with endpoints at (2,3) and (6,7), construct its perpendicular bisector and find its intersection with the x-axis.

Answer: Equation of bisector and intersection point

Question 10: Identify and correct the mistake in this construction: The student attempted to bisect a segment using only a ruler and no compass. Explain the error and describe the correct method.

Answer: Incorrect method identified; correct compass method explained

Question 11: Challenge: Construct a triangle with sides 5 cm, 6 cm, and 7 cm. Then, find the circumcenter by constructing the perpendicular bisectors of two sides. Describe the process and verify the point is equidistant from all vertices.

Answer: Construct bisectors, locate circumcenter, verify distances