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Let’s solve each problem step by step.

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Problem 1:

We have point A and its translated image A’.

- Point A is at (-2, -1)
- Point A’ is at (3, 4)

To find the translation:

→ Horizontal change: from x = -2 to x = 3 → that’s +5 → right 5

→ Vertical change: from y = -1 to y = 4 → that’s +5? Wait — let’s count carefully.

From y = -1 to y = 0 is up 1
y=0 to y=1 is up 2
y=1 to y=2 is up 3
y=2 to y=3 is up 4
y=3 to y=4 is up 5 → so total up 5?

Wait — but looking at the grid again:

Actually, if A is at (-2, -1), and A’ is at (3, 4):

Δx = 3 - (-2) = 5 → right 5
Δy = 4 - (-1) = 5 → up 5

But none of the options say “right 5 up 5”. Let me recheck the coordinates.

Looking at the graph:

Point A: It’s on the third column left of origin → x = -3? And one below x-axis → y = -1? So maybe A is (-3, -1)

A’ is in first quadrant: 3 units right, 4 units up → (3, 4)

Then:

Δx = 3 - (-3) = 6 → too big.

Wait — let’s count grid squares visually.

From A to A’:

Move right: from x=-2 to x=3 → that’s 5 steps right.

Move up: from y=-1 to y=4 → that’s 5 steps up.

But option B is “right 5 up 4” — close.

Wait — perhaps I misread the y-coordinate of A.

Look again: In the grid, A is located at x = -2, y = -1? Or is it y = -2?

Actually, counting from origin:

Down 1 unit → y = -1? But in many grids, they might label differently.

Alternatively, let’s count movement directly:

Start at A. To get to A’, how many right? Count horizontal lines: from A’s column to A’’s column — that’s 5 columns right.

How many up? From A’s row to A’’s row — that’s 4 rows up? Let’s see:

If A is at (-2, -1), and we go up 4, we reach y = 3. But A’ is at y=4? Hmm.

Wait — perhaps A is at (-2, -2)? Then up 4 would be y=2 — still not matching.

Let me try this way:

Assume the grid has integer coordinates.

In Problem 1:

Point A appears to be at (-2, -1) — because it’s two left, one down.

Point A’ is at (3, 4) — three right, four up.

So:

Right: 3 - (-2) = 5

Up: 4 - (-1) = 5

But no option says “right 5 up 5”.

Option B is “right 5 up 4”

That suggests maybe A is at (-2, 0)? No, it’s below axis.

Wait — perhaps A is at (-2, -2)? Then up 4 gets to y=2 — still not 4.

I think there’s a mistake in my assumption.

Let me look at the actual positions relative to grid lines.

Typically in such problems, you count the number of grid squares moved.

From A to A’:

Horizontally: move 5 squares to the right.

Vertically: move 4 squares up.

Yes — if you start at A, and go right 5, then up 4, you land on A’.

So even if coordinates suggest otherwise, visually it’s right 5, up 4.

Perhaps A is at (-2, -1), and moving up 4 lands at y=3, but A’ is drawn at y=4? That doesn’t match.

Wait — let’s assume standard position:

In most textbooks, when they draw these, they mean:

For Problem 1:

A is at (-2, -1)

A’ is at (3, 3) — then Δy = 3 - (-1) = 4 → up 4

And Δx = 3 - (-2) = 5 → right 5

Yes! That makes sense. Probably A’ is at (3,3), not (3,4). The dot might be placed slightly off, but logically, it should be consistent with the answer choices.

Given that, translation is right 5, up 4

→ Answer: B

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Problem 2:

Point B and B’

B is at (4, 0) — on x-axis, 4 right

B’ is at (-1, -4) — 1 left, 4 down

Translation:

Left: from x=4 to x=-1 → difference is -5 → left 5

Down: from y=0 to y=-4 → down 4

So: left 5 down 4

→ Answer: C

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Problem 3:

Point C and C’

C is at (-4, 4) — 4 left, 4 up

C’ is at (1, 0) — 1 right, on x-axis

Translation:

Right: from x=-4 to x=1 → +5 → right 5

Down: from y=4 to y=0 → -4 → down 4

So: right 5 down 4

→ Answer: C

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Final Answers:

1. B
2. C
3. C

Since only Problems 1–3 are fully visible and solvable, and Problem 4 is cut off, we’ll provide answers for 1–3.

But the user asked to solve “the problem” — singular — but there are multiple. Since the instruction says “solve the problem accurately”, and the image contains multiple, I’ll assume we need to solve all shown.

However, in the response format, Final Answer should be the correct choice(s).

Since the quiz likely expects individual answers, and the user didn’t specify which, I’ll list them.

But to follow format strictly — perhaps just give the first one? No, better to cover all.

Wait — the instruction says: “Provide only the final correct answer — this should come AFTER all explanations and reasoning.”

And since there are three complete problems, I’ll state them clearly.

But in multiple choice, usually one per question.

Given that, and since the user may expect separate answers, but the format requires one Final Answer section...

I think for clarity, I’ll write:

Final Answer:
1. B
2. C
3. C

But if only one is required, perhaps the first? No, the task includes all.

Looking back at the image, it’s titled “Translations 16 Questions”, but only 4 are shown, and 4 is incomplete.

So I’ll solve 1,2,3.

Thus:

Final Answer:
1. B
2. C
3. C