Question

select the correct answer. given line ab and a point p that is not on line ab, which step is part of constructing a perpendicular line to line ab from point p using a pencil tied to a string? secure push - pin at point p. set string length past the line. secure push - pin at point a on the line. set string length from point a to point p. secure push - pin at point a on the line. set string length past point p. secure push - pin at point p. set string length from point p to the line.

Explanation:

To construct a perpendicular from point \( P \) (not on line \( AB \)) to line \( AB \) using a pencil - tied - to - a - string method (a rough - and - ready compass - like construction), we first need to fix the string at a point on the line \( AB \). Point \( A \) is on line \( AB \), and we need to set the string length such that we can create arcs or a perpendicular. Securing the push - pin at point \( A \) (on line \( AB \)) and setting the string length from \( A \) to \( P \) makes sense because this length will be used to create symmetric arcs or the perpendicular.

• Option 1: Securing at \( P \) and setting length past the line is incorrect as we need to start from the line.
• Option 2: Setting length past \( P \) when secured at \( A \) is not the right approach for perpendicular construction.
• Option 3: Securing push - pin at \( A \) (on line \( AB \)) and setting string length from \( A \) to \( P \) is a correct initial step for this construction.
• Option 4: Securing at \( P \) and setting length to the line is not the correct way to start the perpendicular construction.

Answer:

C. Secure push - pin at point \( A \) on the line. Set string length from point \( A \) to point \( P \).