Which statement explains the relationship of sides ba and b’a’ after rectangle badc has been rotated 180° about the origin?

option b. side b'a' has a slope of 1 and is parallel to side ba.

explanation:

the choices presented in the comments are:

a. side b’a’ has a slope of -1 and is perpendicular to side bab. side b’a’ has a slope of 1 and is parallel to side bac. side b’a’ has a slope of 1 and is perpendicular to side bad. side b’a’ has a slope of -1 and is parallel to side ba

the end points of the side ba are b (1,3) and a (3,5). the slope of this side is:

slope = rise / run = δy / δx = (5 - 3) / (3 - 1) = 2 / 2 = 1.

after been rotated 180° about the origin, the coordinates of the corresponding vertex of each side of the image will be transformed according to the rule (x, y) → (-x, -y).

thus, the images of the vertices b (1,3) and a (3,5) will be b'(-1,-3) and a' (-3, -5), and the slope of the new side b'a' will be:

slope = rise / run = δy / δx = (- 5 - (-3) ) / (-3 - (-1) ) = - 2 / (- 2) = 1.

two lines are parallel if and only if their slopes are equal.

then, you have obtained that both sides ba and b'a' have the same slope, equal to 1, which means that they are parallel, and that the correct choice is the second one: "b. side b’a’ has a slope of 1 and is parallel to side ba".

Answers4.) -1/205.) -1/406.) -55/127.) -3/4

So confused right here i need it to be more clearer