Question

Translate the triangle. Then enter the new coordinates. A(-3, 4) A'([?], [?]) B'([ ], [ ] C([],[]) B(0, 1) C(-4,1)

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Answer 1

The new coordinates are
`A'(x,y) = (3, 0)`,
`B'(x,y) = (6, -3)` and
`C'(x,y) = (2, -3)`.

Explanation:

Vectorially speaking, the translation of a point can be defined by the following expression:

`V'(x,y) = V(x,y) + T(x,y)` (1)

Where:

`V(x,y)` - Original point.

`V'(x,y)` - Translated point.

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

If we know that
`A(x,y) = (-3,4)`,
`B(x,y) = (0,1)`,
`C(x,y) = (-4,1)` and
`T(x,y) = (6, -4)`, then the resulting points are:

`A'(x,y) = (-3, 4) + (6, -4)`

`A'(x,y) = (3, 0)`

`B'(x,y) = (0,1) + (6, -4)`

`B'(x,y) = (6, -3)`

`C'(x,y) = (-4, 1) + (6, -4)`

`C'(x,y) = (2, -3)`

The new coordinates are
`A'(x,y) = (3, 0)`,
`B'(x,y) = (6, -3)` and
`C'(x,y) = (2, -3)`.