Me in geometry!
in the step shown of the construction of a line through a point that is perpendicular to the given line, why must the compass point be placed on points a and b? how would the construction be different if the compass point were placed at random points on the original line?

The compass point must be placed on points A and B because you need to make arcs which would allow you to make the perpendicular line through the given line. The construction would be different if the compass point were placed at random points on the original line because then the line would not be lined up correctly in the middle and it will not be correct, hence why you need to put the compass on A and 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'.

3/6 chance

step-by-step explanation:

half of the nubers are odd numbers (1,3,5) which in that case if you would be told to simplify it would be 1/2