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XYZ has coordinates X(2, 3), Y(1,4), and Z(8,9). A translation maps X to X'(4,7). What are the coordinates for Y' and Z' for this translation?​

Sagot :

xero099

Answer:

The coordinates are [tex]Y'(x,y) = (3, 8)[/tex] and [tex]Z'(x,y) = (10, 13)[/tex].

Step-by-step explanation:

First, we have to derive an expression for translation under the assumption that each point of XYZ experiments the same translation. Vectorially speaking, translation from X to X' is defined by:

[tex]X'(x,y) = X(x,y) + T(x,y)[/tex] (1)

Where [tex]T(x,y)[/tex] is the vector translation.

If we know that [tex]X(x,y) = (2,3)[/tex] and [tex]X'(x,y) = (4,7)[/tex], then the vector translation is:

[tex]T(x,y) = X'(x,y)-X(x,y)[/tex]

[tex]T(x,y) = (4,7) - (2,3)[/tex]

[tex]T(x,y) = (2, 4)[/tex]

Then, we determine the coordinates for Y' and Z':

[tex]Y'(x,y) = Y(x,y) + T(x,y)[/tex]

[tex]Y'(x,y) = (1,4) + (2,4)[/tex]

[tex]Y'(x,y) = (3, 8)[/tex]

[tex]Z'(x,y) = Z(x,y) + T(x,y)[/tex]

[tex]Z'(x,y) =(8,9) + (2,4)[/tex]

[tex]Z'(x,y) = (10, 13)[/tex]

The coordinates are [tex]Y'(x,y) = (3, 8)[/tex] and [tex]Z'(x,y) = (10, 13)[/tex].

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