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MrRa [10]
2 years ago
9

In the coordinate plane, the point A, 4− 2 is translated to the point A′, 1− 5. Under the same translation, the points B, 7− 4 a

nd C, 2− 5 are translated to B′ and C′, respectively. What are the coordinates of B′ and C′?
Mathematics
1 answer:
Inga [223]2 years ago
5 0

Answer:

The coordinates of B' and C' are B'(x,y) = (4, -7) and C'(x,y) = (-1, -8), respectively.

Step-by-step explanation:

From the Linear Algebra, we define the translation of a given point as:

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

Where:

O(x,y) - Original point, dimensionless.

T(x,y) - Translation vector, dimensionless.

O'(x,y) - Translated point, dimensionless.

If we know that A'(x,y) = (1, -5) and A(x,y) = (4,-2), then the translation vector is:

T(x,y) = A'(x,y)-A(x,y) (2)

T(x,y) = (1,-5)-(4,-2)

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

If we know that B(x,y) = (7,-4), C(x,y) = (2,-5) and T(x,y) = (-3,-3), then the translated points are, respectively:

B'(x,y) = B(x,y)+T(x,y) (3)

B'(x,y) = (7,-4) +(-3,-3)

B'(x,y) = (4, -7)

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

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

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

The coordinates of B' and C' are B'(x,y) = (4, -7) and C'(x,y) = (-1, -8), respectively.

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