Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

The image of a point is given by the rule [tex]$r_{y=-x}(x, y) \rightarrow(-4, 9)$[/tex]. What are the coordinates of its pre-image?

A. [tex]$(-9, 4)$[/tex]

B. [tex]$(-4, -9)$[/tex]

C. [tex]$(4, 9)$[/tex]

D. [tex]$(9, -4)$[/tex]

Sagot :

GinnyAnswer
To find the coordinates of the pre-image of the point under the transformation rule [tex]\(r_{y=-x}\)[/tex], let's examine the given rule.

The rule [tex]\(r_{y=-x}(x, y) \rightarrow (-y, -x)\)[/tex] indicates that under this transformation:
- The x-coordinate becomes the negation of the y-coordinate.
- The y-coordinate becomes the negation of the x-coordinate.

We are given that the point transforms to [tex]\( (-4, 9) \)[/tex].

Now, reverse the transformation to find the pre-image:
- The x-coordinate of the pre-image will be the negated y-coordinate of the image.
- The y-coordinate of the pre-image will be the negated x-coordinate of the image.

Given the image [tex]\( (-4, 9) \)[/tex]:
- The x-coordinate of the pre-image will be [tex]\(-9\)[/tex] (negation of 9).
- The y-coordinate of the pre-image will be [tex]\(4\)[/tex] (negation of -4).

Thus, the coordinates of the pre-image are [tex]\( (-9, 4) \)[/tex].

Therefore, the correct answer is:
[tex]\[ \boxed{(-9, 4)} \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.