Are the ratios 3:6 and 1:9 equivalent?

No

Step-by-step explanation:

The ratio would have to be 1:2 or 6:12 or with other factors of the two numbers but the numbers have to be multiplied or divided by the same number to get to those factors in order for them to remain equivalent.

For example: If you were to multiply the 3 by 2 but the 6 by three you'd get 6:18 which simplified is 3:9 not 3:6 but if you multiply both the 3 and the 6 by 3 you'd get 9:18 with can by simplified to 3:6

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'.

16 is the absolute value

step-by-step explanation: