Question

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.

Answer 1

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)`.