Hexagon defghi is translated 8 units down and 3 units to the right. if the coordinates of the pre-image of point f are
(–9, 2), what are the coordinates of f'?

(–17, 5)
(–6, –6)
(–17, –1)
(–12, –6)

(-6,-6)

Explanation:
The xy coordinate grid is shown in the attached image.
As we can see:
1- moving down the the y-axis means that we are moving towards the negative direction. This means that we will subtract the translated units from the original y-value to get the y-value of the image
We are given that the point was translated 8 units down and that the original y-coordinate was 2.
This means that:
y-coordinate of image = y-coordinate of original point - translated units
y-coordinate of image = 2 - 8
y-coordinate of image = -6

2- moving to the right of the x-axis means that we are moving towards the positive direction.This means that we will add the translated units to the original x-value to get the x-value of the image.
We are given that the point was translated 3 units to the right and that the original x-coordinate was -9.
This means that:
x-coordinate of image = x-coordinate of original point + translated units
x-coordinate of image = -9 + 3
x-coordinate of image = -6

Based on the above, the coordinates of the image are (-6,-6)

Hope this helps :)