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gladu [14]
3 years ago
7

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 thi

s translation?​
Mathematics
1 answer:
Rashid [163]3 years ago
7 0

Answer:

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

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:

X'(x,y) = X(x,y) + T(x,y) (1)

Where T(x,y) is the vector translation.

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

T(x,y) = X'(x,y)-X(x,y)

T(x,y) = (4,7) - (2,3)

T(x,y) = (2, 4)

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

Y'(x,y) = Y(x,y) + T(x,y)

Y'(x,y) = (1,4) + (2,4)

Y'(x,y) = (3, 8)

Z'(x,y) = Z(x,y) + T(x,y)

Z'(x,y) =(8,9) + (2,4)

Z'(x,y) = (10, 13)

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

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