Question

surmy 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’?
○ (a, -b)
○ (b, a)
○ (-a, b)
○ (-b, -a)

Explanation:

Step1: Recall reflection over \( y = x \)

The rule for reflecting a point \((x, y)\) over the line \( y = x \) is to swap the \( x \)-coordinate and the \( y \)-coordinate.

Step2: Apply the rule to point \( D(a, b) \)

For point \( D \) with coordinates \((a, b)\), when we reflect it over \( y = x \), we swap \( a \) (the \( x \)-coordinate) and \( b \) (the \( y \)-coordinate). So the new coordinates of \( D' \) will be \((b, a)\).

Answer:

B. \((b, a)\)