Sumy is working in geometry class and is given figure ABCD in the coordinate plane to reflect. The coordinates of point D are (a, b) and she reflects the figure over the line y = x. What are the coordinates of the image D'?

Question

(a, –b)
(b, a)
(–a, b)
(–b, –a)

Answer 1

To reflect a point \(D(a, b)\) over the line \(y = x\), we switch the coordinates of the point. This means the x-coordinate becomes the new y-coordinate and the y-coordinate becomes the new x-coordinate.

So, reflecting the point \(D(a, b)\) over the line \(y = x\) gives us the new coordinates for \(D'\) as:

\[ D' = (b, a) \]

Therefore, the coordinates of the image \(D'\) is:

\((b, a)\)

So the correct answer is \((b, a)\).