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Sumy is given figure [tex][tex]$ABCD$[/tex][/tex] in the coordinate plane to reflect. The coordinates of point [tex][tex]$D$[/tex][/tex] are [tex][tex]$(a, b)$[/tex][/tex] and she reflects the figure over the line [tex][tex]$y=x$[/tex][/tex].

What are the coordinates of the image [tex][tex]$D'$[/tex][/tex]?

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



Answer :

GinnyAnswer
When reflecting a point over the line [tex]\( y = x \)[/tex], the coordinates of the point are swapped. This means that the [tex]\(x\)[/tex]-coordinate and the [tex]\(y\)[/tex]-coordinate exchange places.

Given the coordinates of point [tex]\( D \)[/tex] as [tex]\( (a, b) \)[/tex], after reflecting over the line [tex]\( y = x \)[/tex] we switch the coordinates [tex]\( a \)[/tex] and [tex]\( b \)[/tex].

Therefore, the new coordinates of point [tex]\( D' \)[/tex] (the image of [tex]\( D \)[/tex]) will be [tex]\( (b, a) \)[/tex].

Thus, the correct answer is:
[tex]\[ (b, a) \][/tex]

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