Question

Point P(6, 6) lies on the circle with center (2, 3) and radius 5 coordinate units. Find the co-ordinates of the image of point P after the circle is rotated ${90}^{\circ }$ clockwise $(\circlearrowright )$ about its center.

• A. (2, 3)
• B. (3, 2)
• C. (5, -1)
• D. (6, 0)
• E. (7, 3)

Answer 1

The correct option is C (5, -1)

$Z_p-Z_o=(Z_p-Z_o)e^{i\theta }$

$Z_p^{\prime }-Z_o=(Z_p-Z_o)e^{i(\theta -{90}^o)}$

$⟹\frac{Z_p^{\prime }-Z_o}{Z_p-Z_o}=e^{-i{90}^o}$

$⟹Z_p^{\prime }=Z_o+(Z_p-Z_o)e^{-i{90}^o}$

$=(2+3i)+[(6+6i)-(2+3i)]e^{-i{90}^o}$

$=(2+3i)+(4+3i)(-i)$

$=2+3i-4i+3=5-i$

Hence, $P^{\prime }=(5,-1)$