A(2,-5) after a translation 3 units left and 6 unit up.
(x,y) → (x-3,y+6)
To find the coordinates of A after a translation of 3 units left and 6 units up, we will subtract 3 from the x-coordinate and add 6 to the y-coordinate.
The translation can be represented by the vector (-3, 6).
To find the new x-coordinate:
New x-coordinate = old x-coordinate - 3
New x-coordinate = 2 - 3
New x-coordinate = -1
To find the new y-coordinate:
New y-coordinate = old y-coordinate + 6
New y-coordinate = -5 + 6
New y-coordinate = 1
Therefore, the new coordinates of A after the translation are (-1, 1).