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)

B. (3, -1)

Step-by-step explanation: I got a 100 on the test

The rule for a reflection across line y = -x: (x, y) → (-y, -x)

F(1, -3) → F'(3, -1)

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)