Question

2. A triangular 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 using the following rule: (x, y, z)  (x + 2, y + 4, z – 3). Determine the coordinates of that final image, following these steps:
1. Write the general rule you use for the reflection. (4 points)

2. What would be the new points of the shape after this reflection? (4 points)


3. Now, use the points from number 2 and apply the translation rule. Show the results of your calculations for that translation. (4 points)

Answer 1

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)

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2. 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)
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3. Applying the transformation rule (x, y, z) → (x + 2, y + 4, z – 3)

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)