Question

Square OABC is drawn on a centimetre grid. O is (0,0) A is (2,0) B is (2,2) C is (0,2) Write down how many invariant points there are on the perimeter of the square when OABC is rotated 90 degrees clockwise, centre (2,0).

Answer 1

One invariant point;

Point A = (2, 0)

Explanation:

The coordinates of the square vertices are;

O = (0, 0)

A = (2, 0)

B = (2, 2)

C = (0, 2)

Therefore, we have by 90° clockwise rotation;

O' = (2, 2)

A' = (2, 0)

B' = (4, 0)

C' = (2, 4)

Therefore, since only A' (2, 0) = A (2, 0), we have only one invariant point on the perimeter of the square when it is rotated 90° about the center (2, 0) which is the point A = (2, 0).