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Sumy is working in geometry class and is given figure ABCD in the coordinate plane to reflect. The coordinates of point D are [tex]$(a, b)$[/tex] and she reflects the figure over the line [tex]$y = x$[/tex]. What are the coordinates of the image [tex][tex]$D^{\prime}$[/tex][/tex]?

A. [tex]$(a, -b)$[/tex]
B. [tex]$(b, a)$[/tex]
C. [tex][tex]$(-a, b)$[/tex][/tex]
D. [tex]$(-b, -a)$[/tex]

Sagot :

GinnyAnswer
To reflect a point over the line [tex]\( y = x \)[/tex], you need to swap the coordinates of the point.

Given the coordinates of point [tex]\( D \)[/tex] as [tex]\( (a, b) \)[/tex]:

1. Reflecting over the line [tex]\( y = x \)[/tex] involves swapping the [tex]\( x \)[/tex]-coordinate with the [tex]\( y \)[/tex]-coordinate.
2. Therefore, for point [tex]\( D \)[/tex] with coordinates [tex]\( (a, b) \)[/tex], the reflected image [tex]\( D' \)[/tex] will have its coordinates swapped to [tex]\( (b, a) \)[/tex].

So, the coordinates of the image [tex]\( D' \)[/tex] after reflecting point [tex]\( D \)[/tex] over the line [tex]\( y = x \)[/tex] are [tex]\( (b, a) \)[/tex].

Thus, the correct answer is:

[tex]\[ (b, a) \][/tex]
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