Find the missing side lengths, leave your answers as radical in simplest form. ( Please answer ASAP!)

9) a = 8, b = 4√2

10) x = 7√2, y = 7

11) x = 5√2, y = 5

12) a = 10, b = 5√2

Step-by-step explanation:

You can notice all these triangles are special as 45° - 45° - 90° triangles. In 45° - 45° - 90° triangles, the hypotenuse is √2 times the sides. We can set up these equations and solve:

9)

a = 4√2 * √2

a = 8

Since the triangle is isosceles, the legs are the same length, so:

b = 4√2

10)

x = 7 * √2

x = 7√2

Since the triangle is isosceles, the legs are the same length, so:

y = 7

11)

x = 5 * √2

x = 5√2

Since the triangle is isosceles, the legs are the same length, so:

y = 5

12)

a = 5√2 * √2

a = 10

Since the triangle is isosceles, the legs are the same length, so:

b = 5√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'.