the point t' (-4,-7) is the image of point t under a transformation. if point t is (-4,7) what translation could have occurred
It moved up from -7 to +7 so it could be a translation straight down.
It could also be a reflection about the x axis, but the question asks for a "translation".
To determine the translation that could have occurred to transform point T (-4,7) to the point T' (-4,-7), we can use the concept of translations in coordinate geometry.
A translation is a transformation that moves a point a certain distance in a specific direction without changing its orientation or shape. It can be described by the horizontal and vertical shifts.
In this case, we observe that the x-coordinate of point T remains the same in the transformation (from -4 to -4), which implies that there is no horizontal shift. However, the y-coordinate changes from 7 to -7, indicating a vertical shift downwards.
Therefore, the translation that could have occurred is a downward translation of 14 units, since the y-coordinate difference between the original point T (-4,7) and the image point T' (-4,-7) is 14.
In summary, the transformation that could have occurred is a translation of 14 units downwards.