This pre-image was translated 3 units right and 6 units up. Use the segment tool to draw the image.

Let
A( -5,-4) B(-1,-6) C(1,-3)
we know that
the rule of the transformation is
(x,y)---------> (x+3,y+6)
so
Find A'
(-5,-4)---------> (-5+3,-4+6)-------> A' (-2,2)
Find B'
(-1,-6)---------> (-1+3,-6+6)-------> B' (2,0)
Find C'
(1,-3)---------> (1+3,-3+6)-------> C' (4,3)
the answer in the attached figure
Answer:
We are given a pre-image now it is given that the pre-image is translated 3 units right and 6 units up so the change or the rule of the transformation in the coordinates is given by:
(x,y) → (x+3,y+6)
We are given the vertices of the pre-image are:
(-5,-4) , (-1,-6) and (1,-3)
Hence, the transformed image has the vertices aS:
(-5,-4) → (-5+3,-4+6)=(-2,2)
(-1,-6) → (-1+3,-6+6)=(2,0)
and (1,-3) → (1+3,-3+6)=(4,3)
so, the image after translation of the pre-image has vertices:
(-2,2) , (2,0) and (4,3)