In the mentioned exercise, we used a number and a symbol to create a translation that resulted in a given image.
Number:& 3
Symbol:& +
Now we want to explain the meaning of the number and symbol we have chosen. First, let's look at the translation we have created.
Translation
(x, y) → (x + 3, y + 3)
To know what the number and symbol means, let's recall some information about how we can write glide reflections.
Transformations of Figures on a Coordinate Plane
Vertical Translations
Translation up k units, k>0
(x, y) → (x + k, y)
Translation down k units, k>0
(x, y) → (x - k, y)
Horizontal Translations
Translation right h units, h>0
(x, y) → (x, y - h)
Translation left h units, h>0
(x, y) → (x, y + h)
Since our translation changes both coordinates of a point, it is both a vertical and horizontal translation. Let's first consider the vertical part. Since the symbol is +, we know that the figure is translated up. The number is 3, so the figure is translated 3 units.
x → x + 3
translation 3units up
Similarly, if we consider the horizontal portion of our translation, we can notice that the symbol is +, so the figure is translated left, and the number is 3, so the figure is translated 3 units.
y → y + 3
translation 3units left
In general, when considering a translation, the symbol tells us the direction in which the figure moves, and the number tells us how far it moves.
