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Figure ABCDEF was reflected across the line y = –x to create figure A'B'C'D'E'F'. On a coordinate plane, a 6-sided figure has p...Question
Figure ABCDEF was reflected across the line y = –x to create figure A'B'C'D'E'F'.
On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).
What are the coordinates of the pre-image of F'?
(–2, 4)
(4, 2)
(2, –4)
(–4, –2)
On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).
What are the coordinates of the pre-image of F'?
(–2, 4)
(4, 2)
(2, –4)
(–4, –2)
Answers
GPT-4o mini
To find the pre-image of point F' (-4, -2) after a reflection across the line y = -x, we can use the property of reflections.
When a point (x, y) is reflected across the line y = -x, the x and y coordinates are swapped and their signs are changed. Therefore, the formula for finding the pre-image (x', y') from the image (x'', y'') after reflection across the line y = -x is:
\[
(x', y') = (-y'', -x'')
\]
For F', we have:
- F' has coordinates (-4, -2).
Thus, the coordinates of the pre-image F can be calculated as follows:
\[
F = (-(-2), -(-4)) = (2, 4)
\]
So the coordinates of the pre-image of F' are (2, 4).
Among the given options, the correct answer is:
(2, –4) (Note that this is incorrect; the correct option based on our calculation was not provided. The correct coordinates we found are specifically (2, 4). Please check the choices again.) However, if we refer solely to the choices provided and the correct reflection, the only one that is in the closest relation while taking negatives into account might be (–2, 4) but that is incorrect as per our detailed reflection rule.
Thus, the computed answer (2, 4) is indeed the accurate pre-image of F'.
When a point (x, y) is reflected across the line y = -x, the x and y coordinates are swapped and their signs are changed. Therefore, the formula for finding the pre-image (x', y') from the image (x'', y'') after reflection across the line y = -x is:
\[
(x', y') = (-y'', -x'')
\]
For F', we have:
- F' has coordinates (-4, -2).
Thus, the coordinates of the pre-image F can be calculated as follows:
\[
F = (-(-2), -(-4)) = (2, 4)
\]
So the coordinates of the pre-image of F' are (2, 4).
Among the given options, the correct answer is:
(2, –4) (Note that this is incorrect; the correct option based on our calculation was not provided. The correct coordinates we found are specifically (2, 4). Please check the choices again.) However, if we refer solely to the choices provided and the correct reflection, the only one that is in the closest relation while taking negatives into account might be (–2, 4) but that is incorrect as per our detailed reflection rule.
Thus, the computed answer (2, 4) is indeed the accurate pre-image of F'.