For AI agents: use /llms.txt for the Nakafa content index.
Every translation uses the same displacement vector for every point:
For any point , this translation is written as or and is defined by:
This means:
Here, is the horizontal shift (positive to the right, negative to the left) and is the vertical shift (positive upwards, negative downwards).
Translate the point by the following vector and determine its image:
Here, , , , and .
Move two units left and three units up. Add the horizontal and vertical components separately:
The image of point is .
Determine the image of the line under the following translation:
Let be any point on line . Under this translation, its image is where:
Use the original coordinates in the line equation. Substitute these values of and into the equation of line :
Replacing and back to and , the equation of the image line is:
Apply the same vector to every point. For a line equation, express the original coordinates in terms of the image coordinates first. For a triangle, check all three vertices so the shape stays unchanged.
Translate the point by the following vector and determine its image:
Determine the image of the line under the following translation:
A triangle has vertices , , and . Translate it by the following vector and determine the coordinates of :
A negative sign means a shift left or down. In the line equation, use inverse substitution because the original equation describes coordinates before the translation.
Solution 1
For the point , use .
Thus, the image point is .
Solution 2
For the line , use .
Substitute into the line equation:
Image line equation: .
Solution 3
Translate each vertex , , and using .
The coordinates of the image triangle are , , and .
Published: . Updated: .
