Answered

IDNLearn.com provides a user-friendly platform for finding answers to your questions. Get prompt and accurate answers to your questions from our experts who are always ready to help.

Sumy is working in geometry class and is given figure [tex]$ABCD$[/tex] in the coordinate plane to reflect. The coordinates of point [tex]$D$[/tex] 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]$D'$[/tex]?

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

Sagot :

GinnyAnsweridn
When reflecting a point [tex]\((a, b)\)[/tex] over the line [tex]\(y = x\)[/tex], you swap the [tex]\(x\)[/tex]- and [tex]\(y\)[/tex]-coordinates of the point. This means the [tex]\(x\)[/tex]-coordinate of the image will be [tex]\(b\)[/tex] and the [tex]\(y\)[/tex]-coordinate of the image will be [tex]\(a\)[/tex].

Given the coordinates of point [tex]\(D\)[/tex] as [tex]\((a, b)\)[/tex], the steps to find the coordinates of the reflected image [tex]\(D'\)[/tex] are as follows:

1. Start with the coordinates of the original point [tex]\(D\)[/tex], which are [tex]\((a, b)\)[/tex].
2. Reflect the point over the line [tex]\(y = x\)[/tex]; to do this, you swap the [tex]\(x\)[/tex]-coordinate and [tex]\(y\)[/tex]-coordinate.
3. After swapping, the new coordinates are [tex]\((b, a)\)[/tex].

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

Therefore, the correct answer is [tex]\((b, a)\)[/tex].
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.