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Answer:
A) J(-3, 1), ...
Explanation:
All of the answer choices list point J' first, so it is convenient to use that as an example.
Point J on the given graph has coordinates (x, y) = (3, 2). The x-coordinate is 3 because the point is 3 units to the right of the y-axis.
The problem statement tells you to translate this point 6 units to the left. When you move it 6 units left, it will move left 3 units to the y-axis, then left 3 more units to have an x-coordinate of 3 -6 = -3. That is, each unit of movement to the left subtracts 1 from the x-coordinate. The x-coordinate of J is 3, so the final point J' will have an x-coordinate of 3 - 6 = -3.
At this point, you have enough information to make the correct answer selection. Only one answer choice has the x-coordinate of J' as -3.
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The other coordinates are translated using similar logic. The y-coordinate of J is 2. Translating it down 1 unit subtracts 1 from the y-coordinate to make it be 2 -1 = 1. Then the coordinates of J' are (-3, 1).
We write the translation rule as ...
(x, y) ⇒ (x -6, y -1)
This means the coordinates of each translated point have 6 subtracted from the original x-coordinate, and 1 subtracted from the original y-coordinate. The other coordinates of the figure are ...
I(2, 4) ⇒ I'(2 -6, 4 -1) = I'(-4, 3)
H(5, 5) ⇒ H'(5 -6, 5 -1) = H'(-1, 4)
G(4, 1) ⇒ G'(4 -6, 1 -1) = G'(-2, 0)