Translations in math simply mean moving. It means moving a point or a set of points without rotating, resizing, flipping them across a line or anything else. Just moving them.
To translate a shape, all of the points of that shape must move:
1. The same distance
2. The same direction
To translate a shape, all of the points of that shape must move:
1. The same distance
2. The same direction
Take the figure to the left as an example. The original quadrilateral ABCD rests in Quadrant 1. The translation can be written 2 different ways:
1. The figure is translated (slides) 7 units to the left and 3 units down.
2. (x-7 , y-3)
Method 1 simply describes what happens during the translation with words. Method 2 allows you to manipulate the original points of the figure with a formula. For instance:
A= (2 , 4) --> (2-7 , 4-3) --> A'= (-5 , 1)
B= (4 , 4) --> (4-7 , 4-3) --> B'= (-3 , 1)
When we translate a shape, the new points are known as "primes," so when we translate point A, it then becomes A' which is read "A prime." When trying to decipher a translation from a graph, always look for the original figure and see how it moved to get to the prime points.
1. The figure is translated (slides) 7 units to the left and 3 units down.
2. (x-7 , y-3)
Method 1 simply describes what happens during the translation with words. Method 2 allows you to manipulate the original points of the figure with a formula. For instance:
A= (2 , 4) --> (2-7 , 4-3) --> A'= (-5 , 1)
B= (4 , 4) --> (4-7 , 4-3) --> B'= (-3 , 1)
When we translate a shape, the new points are known as "primes," so when we translate point A, it then becomes A' which is read "A prime." When trying to decipher a translation from a graph, always look for the original figure and see how it moved to get to the prime points.
Rules for Translations
When working with formula translations such as (x-3 , y+2), there are a few basic rules for which way to move the points:
X-axis: subtraction means go to the left and addition means go to the right
Y-axis: subtraction means go down and addition means go up
X-axis: subtraction means go to the left and addition means go to the right
Y-axis: subtraction means go down and addition means go up