Point A (5, 12) rotated about the origin O in the XY-plane through an angle of 30^ in the anticlockwise direction to a new position B. The ordinate of point B is...

Step-by-step solution

Let the coordinates of point A be (x, y) = (5, 12) . When a point (x, y) is rotated about the origin by an angle in the anticlockwise direction, the new coordinates (x', y') are given by: x' = x - y y' = x + y Substituting x = 5 , y = 12 , and = 30^ to find the ordinate y' of the new point B: y' = 5 30^ + 12 30^ y' = 5 ( 1 2 ) + 12 ( 3 2 ) y' = 5 2 + 6 3 The ordinate of point B is 6 3 + 5 2 . Answer: 6 3 + 5 2