If AD is 10 inches long BD is 6 inches long

AB = 8 inches

Step-by-step explanation:

given :

AD = 10 inches

BD = 6 inches

AB = ?

using pythagoras theorem

a^2 + b^2 = c^2

BD^2 + AB^2 = AD^2

6^2 + AB^2 = 10^2

36 + AB^2 = 100

AB^2 = 100 - 36

AB^2 = 64

AB =

AB = 8

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'.