Q21 - Geometry

Question

Draw two points P, Q on a sheet of paper. Fold the paper so that fold line f contain both P, Q. Unfold the paper. Now fold so that P falls on Q. Call the second fold g. Lay the paper flat and label the intersection of f and g as X. How are points P, Q and X? Explain.

Step-by-Step Solution

Answer

X is the midpoint of P, Q.

Step 1. Check the statement.

Consider the below statements.

 

Draw two points P and Q on a sheet of paper.

 

Fold the paper so that fold line f contains both points P and Q.

 

Unfold and fold along line P and Q so that point P falls on Q.

 

The second fold is called g.

Step 2. Apply the concept of midpoint.

Midpoint is the point on the segment that divides the segment into two congruent segments.

Step 3. Step description.

The point X is the intersection of line f and Q.

Which lies in the middle of points P and Q as the fold g is done so that points P and Q.

 

From the definition of midpoint is the point on the segment that divides the segment into two congruent segments thus X is the Midpoint.

 

Therefore, X is the Midpoint of P and Q.