Translation Explorer

Extend your learning by practicing translations on the coordinate plane and comparing translations with other transformations.

Watch these lessons to learn how to translate figures on the coordinate plane and describe translations using horizontal and vertical movements.

Use the Translation Explorer to slide a figure across the coordinate plane and connect the movement to a coordinate rule.

Drag the pre-image or move individual vertices to create your own figure. Use the sliders to translate the figure horizontally and vertically.

Compare the original coordinates to the new coordinates to see how every point moves the same distance and direction.

How does moving right or left affect the \(x\)-coordinate?

How does moving up or down affect the \(y\)-coordinate?

What stays the same after a translation? What changes?

Transformation: A change in the position, size, or orientation of a figure.

Translation: A transformation that slides a figure without turning or flipping it.

Slide: Another way to describe a translation.

Pre-image: The original figure before a transformation.

Image: The new figure after a transformation.

Prime Notation: A way to label transformed points. For example, \(A'\) is read as “A prime.”

Rigid Transformation: A transformation that preserves size and shape.

Congruent: Figures that have the same size and shape.

Horizontal Movement: Movement left or right that changes the \(x\)-coordinate.

Vertical Movement: Movement up or down that changes the \(y\)-coordinate.

Coordinate Rule: A rule that describes how coordinates change during a transformation.

Ordered Pair: A pair of numbers \((x,y)\) used to locate a point on the coordinate plane.

A translation moves every point the same horizontal distance and the same vertical distance.

The general rule for a translation is:

\((x,y) \rightarrow (x+a,y+b)\)

The value of \(a\) tells how far the figure moves left or right. The value of \(b\) tells how far the figure moves up or down.

For example, a translation 4 units right and 3 units down can be written as \((x,y) \rightarrow (x+4,y-3)\).

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