Atriangular pyramid begins with these coordinates: p(–1, 2, 0) y(2, 3, 0) r(–3, 4, 0) a(–2, 1, 5) the pyramid is then reflected over the yz-plane. the reflected image is then translated 2 units forward, 4 units right, and 3 units down. determine the coordinates of that final image, following these steps: write the general rule you use for the reflection. show the results of your calculations for the reflection. write the general rule you use for the translation. (hint: begin with the result of the rule for the reflection.) show the results of your calculations for the translation

1. The yz-plane is the plane x = 0. 
So, The general rule of reflection over the yz- plane is (x,y,z) →(−x,y,z)



2. Show the results of your calculations for the reflection

Applying the rule found in (1)
the new points of the shape after this reflection will be

P(–1, 2, 0)  ⇒⇒⇒ P'(1, 2, 0)
Y(2, 3, 0)    ⇒⇒⇒ Y'(-2, 3, 0)
R(–3, 4, 0)  ⇒⇒⇒ R'(3, 4, 0)
A(–2, 1, 5)  ⇒⇒⇒ A'(2, 1, 5)


3. image is translated 2 units forward, 4 units right, and 3 units down

So, the transformation rule (x, y, z) → (x + 2, y + 4, z – 3)
Apply the transformation rule to the points from number 2

P'(1, 2, 0)  ⇒⇒⇒ P" (3 , 6 , -3 )
Y'(-2, 3, 0) ⇒⇒⇒ Y" (0 , 7 , -3)
R'(3, 4, 0)  ⇒⇒⇒ R" ( 5 , 8 , -3)
A'(2, 1, 5)  ⇒⇒⇒ A" ( 4 , 5 , 2)


4. Write the general rule you use for the translation.
The general rule for the translation from the basic shape to the final image.
(x , y , z ) → (-x + 2, y + 4, z – 3)


5. the results of general the translation:
P(–1, 2, 0)  ⇒⇒⇒ P'(1, 2, 0)  ⇒⇒⇒ P" (3 , 6 , -3 )
Y(2, 3, 0)    ⇒⇒⇒ Y'(-2, 3, 0) ⇒⇒⇒ Y" (0 , 7 , -3)
R(–3, 4, 0)  ⇒⇒⇒ R'(3, 4, 0)  ⇒⇒⇒R" ( 5 , 8 , -3)
A(–2, 1, 5)  ⇒⇒⇒ A'(2, 1, 5)  ⇒⇒⇒ A" ( 4 , 5 , 2)