Answer:
T<7, -3>
Explanation:
You want to know all of the information necessary to describe the translation of ΔABC to ΔA'B'C', given C(-1, 4) and C'(6, 1).
Information
The information necessary to describe a translation is ...
A quantity that has both magnitude and direction is called a vector quantity. As with most vectors, a translation vector can be described in different ways.
When the figures are drawn on a coordinate grid, the translation vector is conveniently described by an ordered pair: <units right, units up>. The number of units of translation to the right will be the difference of x-coordinates:
Cx' -Cx = 6 -(-1) = 7 . . . . . the image is 7 units right of the preimage
The number of units of translation up will be the difference of y-coordinates:
Cy' -Cy = 1 -4 = -3 . . . . . the image is 3 units down (-3 up) from the preimage
The translation vector can be written as ...
<7, -3>
Transformation
There are several kinds of transformations that can be applied to geometric figures. In addition to the amount of translation, we must also know that the transformation is a translation. This is sometimes identified using a T as an indicator:
T<7, -3> . . . . . represents a translation 7 units right and 3 units down
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Additional comment
Other kinds of transformation include rotation, reflection, and dilation. Each of these requires different information, and is designated using different conventions. (Sometimes it can be difficult to tell the difference between rotation and reflection, depending on the notation used.)