\( \triangle A B C \), with coordinates \( A(2,-1), B(4,-1), C(2,-3) \), is reflected over the line \( y=x \), what are the coordinates of \( \triangle A^{\prime} B \) \( A^{\prime}(2,1), B^{\prime}(4,1), C(2,3) \) \( A^{\prime}(-1,2), B^{\prime}(-1,4), C(-3,2) \) \( A^{\prime}(-2,1), B^{\prime}(-4,1), C(-2,3) \) \( A^{\prime}(-2,-1), B^{\prime}(-4,-1), C(-2,-3) \)

To find the coordinates of triangle \( A'B'C' \) after reflecting triangle \( ABC \) over the line \( y = x \), we swap the x and y coordinates of each vertex. So, - \( A(2, -1) \) reflects to \( A'(-1, 2) \) - \( B(4, -1) \) reflects to \( B'(-1, 4) \) - \( C(2, -3) \) reflects to \( C'(-3, 2) \) None of the given options are correct as the correct reflection coordinates should be \( A'(-1, 2), B'(-1, 4), C'(-3, 2) \). As for some extra fun facts: The line \( y = x \) is known to have interesting properties, such as being the line of symmetry for any point that lies on it. Reflecting over this line is like flipping a pancake: you want the edges to match up! Isn’t it fun to think of math in cooking terms? When reflecting points, a common mistake is forgetting to change the signs when necessary, especially if you're working in quadrants where coordinates can be negative. Always double-check that you’re flipping those axes correctly and maybe practice with a few points on graph paper for visual confirmation!