Question

question 13 of 25

using paper folding to construct a line perpendicular to a given line through a point, fold the paper through the point so that the given line segment lies

a. on the point.
b. at an angle.
c. upon itself.
d. perpendicular to the papers edge.

Explanation:

Identify the geometric goal

The objective is to construct a line perpendicular to a given line through a given point using paper folding.

Analyze paper folding mechanics

Using the Paper Folding Constructions knowledge point:
To create a perpendicular crease relative to a given line, we must fold the paper so that the given line segment lies directly onto itself. This folding action ensures that the angle formed by the crease and the line is bisected into two equal angles that sum to \(180^\circ\), creating a \(90^\circ\) (perpendicular) angle.

Match with the given options

• Option A suggests folding so the line lies "on the point," which does not guarantee perpendicularity.
• Option B suggests folding "at an angle," which is too vague.
• Option C suggests folding so the line segment lies "upon itself," which is the precise requirement for perpendicularity.
• Option D suggests folding "perpendicular to the paper's edge," which depends on the orientation of the line relative to the edge and is not a general construction method.

Answer:

• A. on the point.
• B. at an angle.
• C. upon itself. (Correct answer)
• D. perpendicular to the paper's edge.