Answer:
1)
(x,y,z) → (x,-y,z).
2)
P:(0,5,4) → P'(0,-5,4)
Y: (-2, 7, 4) → Y'(-2,-7,4)
R: (0, 7, 4) → R'(0,-7,4)
A: (0, 7, 6) → A'(0,-7,6)
3)
(x',y',z') → (x'-3,y'-2,z'+4).
4)
P:(0,5,4) → P"(-3,-7,8)
Y: (-2, 7, 4) → Y"(-5,-9,8)
R: (0, 7, 4) → R"(-3,-9,8)
A: (0, 7, 6) → A"(-3,-9,10).
Step-by-step explanation:
A triangular pyramid begins with these coordinates:
P: (0, 5, 4)
Y: (-2, 7, 4)
R: (0, 7, 4)
A: (0, 7, 6)
1)
The pyramid is reflected over the xz-plane.
so the rule of the reflection will be:
The points x,y,z are transformed to x,-y,z.
i.e. (x,y,z) → (x',y',z').
where (x'y'z')=(x,-y,z)
i.e. (x,y,z) → (x,-y,z)
2)
The coordinates of the points after reflection is:
P:(0,5,4) → P'(0,-5,4)
Y: (-2, 7, 4) → Y'(-2,-7,4)
R: (0, 7, 4) → R'(0,-7,4)
A: (0, 7, 6) → A'(0,-7,6)
3)
The general rule of translation is:
(x',y',z') → (x'-3,y'-2,z'+4).
4)
Hence, our point P,Y,R and A are given as:
P:(0,5,4) → P''(0-3,-5-2,4+4)=P"(-3,-7,8)
Y: (-2, 7, 4) → Y''(-2-3,-7-2,4+4)=Y"(-5,-9,8)
R: (0, 7, 4) → R''(0-3,-7-2,4+4)=R"(-3,-9,8)
A: (0, 7, 6) → A''(0-3,-7-2,6+4)=A"(-3,-9,10).
i.e.
P:(0,5,4) → P"(-3,-7,8)
Y: (-2, 7, 4) → Y"(-5,-9,8)
R: (0, 7, 4) → R"(-3,-9,8)
A: (0, 7, 6) → A"(-3,-9,10).
