We need to translate this triangle following the rule (x + 6, y - 2), that is, moving the figure six units to the right, and moving the figure 2 units downward.
For doing this, we need to identify the points of the vertices of the triangle ABC:
A(-6, 2)
B(-2, 4)
C(-4, -4)
We need to be careful that each unit on the x-axis and y-axis are equivalent to 2 units.
Then, applying the rule fr the translation, we have:
T ---> (x+6, y-2)
A(-6, 2) ---> A'(-6+6, 2-2) ---> A'(0, 0)
B(-2, 4) ---> B'(-2+6, 4-2) ---> B'(4, 2)
C(-4, -4) ---> C'(-4+6, -4-2) ---> C'(2, -6)
Then, the vertices of the image are:
A'(0, 0)
B'(4, 2)
C'(2, -6)
The image can be represented in the next graph:
In summary, we have that the vertices of the triangle ABC when it is translated by the rule (x+6, y-2) are:
A'(0, 0)
B'(4, 2)
C'(2, -6)
And we can see this transformation in the above graph.
