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

explanation:

the choices presented in the comments are:

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

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:

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".

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: