Question

which of the following constructions would help to construct a line passing through point c that is perpendicular to the line ab? select the correct choice. diagram: line with points a, b, and point c off the line a construction of an equilateral triangle with one side ab b construction of a hexagon with one side bc c construction of a perpendicular bisector through c d construction of a square with one side ab

Explanation:

To construct a line through point \( C \) perpendicular to line \( AB \), we need a construction related to perpendicular bisectors or perpendicular lines through a point. Let's analyze each option:

• Option A: Constructing an equilateral triangle with side \( AB \) doesn't help in drawing a perpendicular to \( AB \) through \( C \).
• Option B: Constructing a hexagon with side \( BC \) is unrelated to drawing a perpendicular to \( AB \) through \( C \).
• Option C: Construction of a perpendicular bisector through \( C \) (specifically, the perpendicular to \( AB \) passing through \( C \)) is the correct construction for this purpose. The perpendicular bisector construction can be adapted to draw a perpendicular line from a point to a given line.
• Option D: Constructing a square with side \( AB \) is not relevant to drawing a perpendicular to \( AB \) through \( C \).

Answer:

C. Construction of a perpendicular bisector through \( C \)