Question 1: Construct a perpendicular from point P to line l using a compass and ruler. Label the foot of the perpendicular as Q.

Answer: Correctly constructed perpendicular with Q on line l

Question 2: Given a point A outside a line l, construct a perpendicular from A to l. Measure the shortest distance from A to l.

Answer: Use compass and ruler to find the perpendicular; distance approximately X units

Question 3: Using a compass, construct a perpendicular bisector of a given segment XY. Explain why this bisector is perpendicular to XY.

Answer: The bisector cuts XY at its midpoint and forms right angles, as proven by the construction

Question 4: Construct a triangle ABC with side AB = 6 cm, and point P such that the perpendicular from P to AB is 4 cm away from A. Find the possible positions of P.

Answer: Two positions of P exist, symmetric about AB, each 4 cm from A, satisfying the perpendicular distance

Question 5: Construct a perpendicular from a point outside a circle to the circle's circumference. Describe the steps and the significance of this construction.

Answer: The perpendicular from the point intersects the circle at the closest point, useful for tangent constructions

Question 6: Construct a perpendicular from point C to the line AB, where C is not on AB. Then measure the length of the perpendicular segment.

Answer: Perpendicular segment length approximately X units

Question 7: A boat is anchored at point P on a river bank (line l). The boat must stay directly perpendicular to line l at all times. Describe how to construct this perpendicular using only a compass and ruler from a known point on the bank.

Answer: Construct perpendicular from known point on line l, then locate boat position at P along this perpendicular

Question 8: Identify and correct the mistake in the following construction: A student tries to construct a perpendicular from point P to line l by copying an angle from another figure.

Answer: Copying angles does not produce perpendiculars; proper compass and ruler method is required

Question 9: Using a compass, construct a perpendicular bisector of segment AB, then verify that it bisects AB accurately.

Answer: Perpendicular bisector intersects AB at midpoint; verify equal segments on both sides

Question 10: Challenge: Given a triangle with vertices A, B, and C, construct the perpendicular from C to side AB. Extend this to find the perpendicular from C to side AC and compare the two. Explain your findings.

Answer: Students should find both perpendiculars and note their properties; possibly concurrent at the orthocenter