Question

The top of a folding table of dimensions 1 X 1 m consists of two halves hinged together. When folded, one half of the top lies over the other, their edges coinciding (Fig. 10a). To open the table, the folded top should be rotated 90° in a clockwise direction (Fig. 10b), after which both halves are put in position (Fig. 10c). Find the position of the centre of rotation of the table top.

 

Answer 1

Answer: The centre of rotation lies at a distance of 62.5 cm from line AB and a distance of 12.5 cm from line AD.

Explanation:

When the table-top is rotated from position ABCD to position A₁B₁C₁D₁ (Fig. 200), point A moves to point A₁, point

B to point B₁, etc. The lines AA₁ and BB₁ are chords of the arcs along which points A and B move during the rotation of the table-top. The centre of rotation lies at the point of intersection of the lines perpendicular to the midpoints of these chords.