Translation Rule Calculator
Apply translation vector (a,b) to find new coordinates.
Translation Formula
Translated Point: (x,y) + (a,b) = (x+a, y+b)
Notation: (x,y) → (x+a, y+b)
Translation Examples
| Original | Vector (a,b) | Image | Movement |
|---|---|---|---|
| (2,3) | (4,-1) | (6,2) | Right 4, Down 1 |
| (0,0) | (-3,5) | (-3,5) | Left 3, Up 5 |
| (-1,4) | (2,2) | (1,6) | Right 2, Up 2 |
Frequently Asked Questions
What is translation in geometry?
Translation slides all points the same direction and distance. Uses vector notation (a,b) meaning slide right a units, up b units. Every point moves the same amount.
What is a translation vector?
Vector (a,b) describes how far to move. Positive a = right, negative = left. Positive b = up, negative = down. Example: vector (3,-2) means right 3, down 2.
How do I apply translation to a point?
Add vector components to coordinates: (x,y) + (a,b) = (x+a, y+b). Point (2,3) translated by (4,-1) becomes (6,2).
Does translation preserve distance?
Yes. Translation is an isometry. All distances between points stay the same. All angles stay the same. Shape unchanged.
What is composition of translations?
Multiple translations add: (x,y)+(a,b)+(c,d) = (x+a+c, y+b+d). Total translation = sum of all vectors.
How do I translate a polygon?
Apply vector to each vertex. (x1,y1)+(a,b), (x2,y2)+(a,b), etc. Connect translated vertices. All move uniformly.
What is the difference between translation and rotation?
Translation: slides by vector, no rotation. Rotation: turns around point. Translation preserves orientation; rotation may change it.
Can translation move in negative direction?
Yes. Negative a slides left, negative b slides down. Vector (-5,3) means left 5, up 3. All directions possible.
Is translation reversible?
Yes. Apply opposite vector to undo. If translated by (a,b), apply (-a,-b) to reverse. Always invertible.
What is pre-image and image in translation?
Pre-image: original points. Image: translated points. Notation: (x,y) → (x+a, y+b). Arrow shows transformation direction.