Question 1: Construct the perpendicular bisector of a line segment AB with endpoints A(2, 4) and B(8, 4). Indicate the point where it intersects the segment.

Answer: Midpoint at (5, 4); perpendicular bisector passes through (5, 4)

Question 2: A student draws a line segment between points C(3, 2) and D(7, 6). They then attempt to draw a perpendicular bisector but do not find the correct midpoint. What common mistake might they have made? Explain briefly.

Answer: They may have calculated the midpoint incorrectly or drawn the bisector from the wrong point.

Question 3: Given a line segment with midpoint at (4, 5), what is the slope of the perpendicular bisector if the original segment has a slope of 1/2?

Answer: -2

Question 4: Construct a line segment with points at (1, 1) and (5, 5). Draw its perpendicular bisector on the grid. What is the key property of all points on this bisector?

Answer: All points on the bisector are equidistant from both endpoints.

Question 5: Plot the points A(2, 3) and B(6, 7). Find and draw the perpendicular bisector. Mark the midpoint.

Answer: Midpoint at (4, 5); the bisector passes through (4, 5).

Question 6: A student claims that the perpendicular bisector of a segment is always vertical. Is this true? Explain briefly.

Answer: No, it depends on the segment's orientation; it can be vertical, horizontal, or sloped.

Question 7: Calculate the coordinates of the midpoint of the segment with endpoints (3, 8) and (9, 12).

Answer: (6, 10)

Question 8: Identify a common misconception students have when constructing the perpendicular bisector and suggest a way to correct it.

Answer: Students often draw the bisector through the endpoints rather than at the midpoint; remind them to find and mark the midpoint first.

Question 9: Construct the segment with endpoints at (-2, -3) and (4, 5). Find the equation of the perpendicular bisector.

Answer: Midpoint at (1, 1); slope of segment = (5+3)/(4+2)=8/6=4/3; perpendicular slope = -3/4; equation passes through (1,1): y-1 = (-3/4)(x-1).

Question 10: In a real-world context, a farmer wants to set up a water sprinkler exactly midway between two apple trees at points (10, 5) and (20, 15). How should they locate the sprinkler?

Answer: They should place the sprinkler at the midpoint (15, 10), which is equidistant from both trees.