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A triangular prism has vertices at A(2,-1,-1) B(2,1,4) C(2,2,-1) D(-1,-1,-1) E(-1,1,4), and F(-1,2,-1)?
This question has two parts:
1 - Which image point has the coordinates (-3,2,1) after a translation using the vector <-5,1,3>
I'm thinking it's point B.
2 - What point represents a reflaction of B over the yz plane?
Of the multiple choice, the four answers did not provide the one I came up with. (I had B'(-2,2,4).) They gave me
A - (-2,-1,4)
B - (-2,1,4)
C - (-2,2,-4)
D - (-2,1,-4)
Which one should it be and why?
To answer both parts of the question, we can use vector operations and basic transformation principles. Let's go through each part separately:
1 - To perform a translation of a point using a vector, we add the vector's components to the coordinates of the point.
Given the vector <-5,1,3> and the point B(2,1,4), the translated coordinates of a point will be:
B' = B + <-5,1,3>
= (2,1,4) + (-5,1,3)
= (-3,2,7)
Therefore, the image point with coordinates (-3,2,7) is B', not B. So, your choice in part 1 is incorrect.
2 - To reflect a point over the yz-plane, we simply negate the x-coordinate of the point while keeping the y and z-coordinates unchanged.
Given the point B(2,1,4), the reflection of B over the yz-plane will be:
B' = (-2,1,4)
Among the choices you provided, the correct answer would be B - (-2,1,4). This coordinate represents the reflection of point B over the yz-plane
In summary, the correct answers are:
1 - The image point with coordinates (-3,2,7) is B', not B.
2 - The point representing the reflection of B over the yz-plane is B - (-2,1,4).