Translation of a Point

Translation of a Point

How to find the point under the given translation: formula, example, and its solution.

Formula

The image of a point (x, y) under the translation (x, y) -> (x + a, y + b) is (x + a, y + b).

The image of a point (x, y)
under the translation (x, y) → (x + a, y + b)
is (x + a, y + b).

Unlike the translation of a function,
write +a and +b.

Translation of a function

Example

Graph the given triangle and its image under the translation (x, y) -> (x + 7, y + 5) on the coordinate plane. Triangle ABC with vertices A(-2, 1), B(2, 3), and C(0, -1)

The translation is (x, y) → (x [+ 7], y [+ 5]).

The image of A(-2, 1) is
A'(-2 [+ 7], 1 [+ 5])
= (5, 6).

The image of B(2, 3) is
B'(2 [+ 7], 3 [+ 5])
= (9, 8).

The image of C(0, -1) is
C'(0 [+ 7], -1 [+ 5])
= (7, 4).

ABC has vertices
A(-2, 1), B(2, 3), and C(0, -1).

A'B'C' has vertices
A'(5, 6), B'(9, 8), and C'(7, 4).

Use these vertices
to draw △ABC and its image △A'B'C'
on the coordinate plane.

As you can see,
A'B'C' is under the translation
(x, y) → (x [+ 7], y [+ 5]).

The triangle is only moved.
There's no change in its size.

So, under a translation,
the length and the area are reserved.