Question

A triangular pyramid begins with its vertices locate at the following points: P (0, 5, 5), Q (-2, 7, 5), R (0, 7, 5), and A (0, 7, 7). The pyramid is then reflected over the xz-plane.
(a) Write the general rule you use for the reflection.

(b) Show the results of your calculations for the reflection.

The reflected image is then translated 2 units back, 4 units right, and 1 unit down.

(c) Write the general rule you use for the translation.

(d) Show the results of your calculations for the translation. (Hint: Begin with the result of the rule for the reflection from (b))

Answer 1

Reflection about the x-z plane means that both x and z coordinates remain unchanged, only the y-coordinate has the sign reversed.
That means:
s(x,y,z)->(x,-y,z).
For example,
s(0,5,5)->(0,-5,5).
You can figure the remaining three points similarly.
For parts C and D,
not sure if "back, right, down" refer to x, y and z axes, or another combination. They must be specified explicitly in words or defined by a diagram.