In parallelogram lmno, mp = 21 m, lp = (y + 3) m, np = (3y – 1) m, and
op = (2x – 1) m.

parallelogram l m n o is shown. diagonals are drawn from point m to point o and from point l to point n and intersect at point p.

what are the values of x and y?

x=11,  y=2

Step-by-step explanation:

MP=OP

2x-1=21

x=11

LP=NP

y+3=3y-1

y=2

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'.