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In the coordinate plane, the point A(3,4) is translated to the point A(6,2). Under the same translation, the points B(1,6) and C(5,1) are translated to B and C, respectively. What are the coordinates of B and C.

User Ndkrempel
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Answer:

The coordinates of B' and C' are
B'(x,y) = (4,4) and
C'(x,y) = (8, -1).

Explanation:

Vectorially speaking, the translation of a point is represented by the following operation:


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

Where:


P(x,y) - Original point.


P'(x,y) - Translated point.


T(x,y) - Translation vector.

First, we need to calculate the translation vector after knowing that
A(x,y) = (3,4) and
A'(x,y) = (6,2). That is:


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


T(x,y) = (6,2) - (3,4)


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

Finally, we determine the coordinates of points B' and C':


B(x,y) = (1,6),
T(x,y) = (3, -2)


B'(x,y) = (1,6) + (3,-2)


B'(x,y) = (4,4)


C(x,y) = (5,1),
T(x,y) = (3, -2)


C'(x,y) = (5,1) + (3,-2)


C'(x,y) = (8, -1)

The coordinates of B' and C' are
B'(x,y) = (4,4) and
C'(x,y) = (8, -1).

User Emillie
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