Given \( \triangle A B C \) has vertices at - \( A(2,2), B(4,5) \), and \( C(6,3) \), and if the \( \Delta \) is first reflected over the \( y \)-axis and then over the \( x \)-axis, find the new coordinates of the \( A^{n} \). Select one: a. \( (-1,-1) \) b. \( (-2,4) \) c. \( (3,-2) \) d. \( (-2,-2) \)

To find the new coordinates of point \( A(2,2) \) after reflecting over the \( y \)-axis and then over the \( x \)-axis, we will carry out the reflections step by step. 1. **Reflect over the \( y \)-axis**: The reflection of any point \( (x, y) \) over the \( y \)-axis is given by \( (-x, y) \). Therefore, reflecting \( A(2,2) \) over the \( y \)-axis gives us: \[ A'( -2, 2) \] 2. **Reflect over the \( x \)-axis**: The reflection of any point \( (x, y) \) over the \( x \)-axis is given by \( (x, -y) \). Now reflecting \( A'(-2, 2) \) over the \( x \)-axis results in: \[ A''(-2, -2) \] So the new coordinates of point \( A \) after both reflections are \( (-2, -2) \). The correct answer is: d. \( (-2,-2) \)