(transforming Coordinates) I do not understand what a translation is that moves the coordinates of an image to two differents points on a x and y axis
A translation in the context of moving coordinates involves shifting the position of an image or object in a specified direction on a coordinate plane. It involves moving all the points of the object to a new location without changing their orientation or shape.
To understand how a translation works, let's consider an example. Suppose we have a point with original coordinates (x, y) on a coordinate plane. Translating the point by a certain amount in the x-axis and y-axis will change its position to new coordinates (x + a, y + b), where 'a' represents the translation amount in the x-axis and 'b' represents the translation amount in the y-axis.
Here's how you can perform a translation of coordinates manually:
1. Identify the original coordinates of the point you want to translate (x, y).
2. Determine how much you want to move the point in the x-axis (let's call it 'a') and the y-axis (let's call it 'b').
3. Add 'a' to the x-coordinate and 'b' to the y-coordinate to find the new coordinates of the point: (x + a, y + b).
For example, suppose we want to translate the point (2, 3) by moving it 4 units to the right and 2 units up. Applying the translation formula:
New x-coordinate = 2 + 4 = 6
New y-coordinate = 3 + 2 = 5
Thus, the new coordinates of the translated point are (6, 5).
Remember that the translation is applied uniformly to all points of the object. So if you have a set of coordinates representing an image or any other object, you would apply the same translation values (a, b) to all the points in the object to achieve the translation effect.