Surface Area and Volume, please help me!

Question

A triangular pyramid begins with its vertices locate at the following points: P(0,5,4) Y(-2,7,4) R(0,7,4) and A(0,7,6).

the pyramid is then reflected over the xz-plane. The reflected image is then translated 3 units back, 2 units left, and 4 units up.

1) write the general rule you use for the reflection

2) Show the results of your calculations for the reflection

3) write the general rule for the translation (Begin with the result of the rule for the reflection)

4) show the results of your calculations for the translation

Answer 1

Vertices of the triangular pyramid are , ,  and .

Pyramid is reflected over XZ plane.

(1)

General rule for the reflection:

The reflection in the xz plane changes the sign of the y coordinate.

  is reflected about XZ plane then the image is .

(2)

Thus, results of reflected images of vertices are  , ,   and .

Answer 2

Result of the reflection is .

3)

Result of the reflection is .

General rule for the translation:

Image translated forward or backward refers to the X-coordinate change.

Image translated left or right refers to the y-coordinate change.

Image translation up or down refersto the z-coordinate change.

4)

Reflected images are  , ,   and .

The reflected image is then translated 3 units back, 2 units left, and 4 units up.

Therefore, subtract 3 from X-coordinate, 2 from Y-coordinate and add 4 units to Z- coordinate of each image.

Thus, the results of translation are , , and .