For AI agents: use /llms.txt for the Nakafa content index.
Translation, also known as a shift or slide, is a type of geometric transformation that moves every point of an object a certain distance in a specified direction. This transformation does not change the orientation, size, or shape of the object; only its position changes.
Given any point . The translation associated with the vector for point , written as or , is defined as:
This means:
Here, is the horizontal shift (positive to the right, negative to the left) and is the vertical shift (positive upwards, negative downwards).
A point is translated by the vector . Determine the image point of this translation.
Here, , , , and .
Using the formula:
Thus, the image of point is .
Determine the image of the line translated by the vector .
Let be any point on line . If translated by the vector , its image is where:
Substitute these values of and into the equation of line :
Replacing and back to and , the equation of the image line is:
Point , vector . .
Thus, the image point is .
Line , vector . .
Points , , . Vector .
Substitute into the line equation:
Image line equation: .
The coordinates of the image triangle are , , and .
