Question
On a coordinate plane, a straight line and a parallelogram are shown. The straight line has a negative slope and has a formula of y = negative x. The parallelogram has points G (negative 2, negative 3), F (1, negative 3), E (negative 1, negative 5), and H (2, negative 5).
What are the coordinates of the image of vertex F after a reflection across the line y = –x?
(–1, –3)
(3, –1)
(1, 3)
(–3, 1)
What are the coordinates of the image of vertex F after a reflection across the line y = –x?
(–1, –3)
(3, –1)
(1, 3)
(–3, 1)
Answers
GPT-4o mini
To find the coordinates of the image of vertex F (1, -3) after a reflection across the line \(y = -x\), we can use the following rule for reflecting a point across that line: the coordinates of the reflected point are obtained by swapping the x and y coordinates and changing their signs.
1. Start with point F:
\[
F (1, -3)
\]
2. Applying the rule:
- Swap the coordinates: \((-3, 1)\)
Thus, the coordinates of the image of vertex F after reflection across the line \(y = -x\) are \((-3, 1)\).
Therefore, the correct answer is \((-3, 1)\).
1. Start with point F:
\[
F (1, -3)
\]
2. Applying the rule:
- Swap the coordinates: \((-3, 1)\)
Thus, the coordinates of the image of vertex F after reflection across the line \(y = -x\) are \((-3, 1)\).
Therefore, the correct answer is \((-3, 1)\).