Question

If on the circle C, the distance from P(1,0) to the point T is x, determine the coordinates for T' if T(3/5,4/5) and T'= pie+x

Answer 1

The coordinates of T' are (-3/5,-4/5)

Explanation:

Assuming that points P, T and T' are on a circle and the circle is centered on (0,0), coordinate of P indicates that the radius of the circle is 1. The distance from P to the point T means the arclength from P to T is x. In the case of a unit circle, the arclength is equal to the radian angle. The arclength from P to the point T' is π + x radians. Then the arclength from T to T' is π radians. This is equivalent to a rotation about the origin, which consist in transform coordinate (x, y) into (-x, -y). In consequence, if the coordinates of T are (3/5,4/5) then the coordinates of T' are (-3/5,-4/5).