Translate a Point by a Vector

Translate a point by a vector

A translation moves a point without changing its shape, size, or orientation. You only shift the point by the vector’s horizontal and vertical components.

Method

1. Read the point’s coordinates, usually written as ((x, y)).
2. Read the vector as a pair of changes, for example ((a, b)).
3. Add the vector to the point coordinate-by-coordinate:
   • new (x = x + a)
   • new (y = y + b)
4. Write the translated point in simplified form.

What the components mean

• A positive first component moves right.
• A negative first component moves left.
• A positive second component moves up.
• A negative second component moves down.

Quick check

Make sure each coordinate changes in the correct direction. If the vector is ((0, b)), only the vertical coordinate should change. If the vector is ((a, 0)), only the horizontal coordinate should change.

Example structure

If a point ((x, y)) is translated by ((a, b)), the result is ((x+a, y+b)). Always verify the signs before simplifying your answer.