Which of the following represents a rotation of △LMN, which has vertices L(4,5), M(0,2), and N(−2,−4), about the origin by 180°? Answers
a)
L (−4, −5)
M (2, 4)
N (0, −2)

b)
L (−5, −4)
M (−2, 0)
N (4, 2)

c)
L (−4, −5)
M (0, −2)
N (2, 4)

b

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8