Sumy is working in geometry class and is given figure ABCD in the coordinate plane to reflect. The coordinates of point D are (a, b) and she reflects the figure over the line y = x. What are the coordinates of the image D'? (a, –b) (b, a) (–a, b) (–b, –a)Sumy is working in geometry class and is given figure ABCD in the coordinate plane to reflect. The coordinates of point D are (a, b) and she reflects the figure over the line y = x. What are the coordinates of the image D'? (a, –b)
(b, a)
(–a, b)
(–b, –a)

(b, a)

Step-by-step explanation:

Example if D was (3, 2) and reflects across y = x, D' will be (2, 3)

answer: 32.68

step-by-step explanation:

x=2

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1