Distance Between Two Points Worksheet for 9th - 12th Grade ... - Free Printable

Let’s solve this step by step.

We are asked to find the distance between two points: (8, 8) and (3, 5).

To find the distance between two points on a coordinate plane, we use the Distance Formula:

> Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Let’s label our points:
- Point 1: (x₁, y₁) = (8, 8)
- Point 2: (x₂, y₂) = (3, 5)

Now plug into the formula:

Step 1: Find the difference in x-coordinates:
x₂ - x₁ = 3 - 8 = -5

Step 2: Find the difference in y-coordinates:
y₂ - y₁ = 5 - 8 = -3

Step 3: Square both differences:
(-5)² = 25
(-3)² = 9

Step 4: Add the squares:
25 + 9 = 34

Step 5: Take the square root:
√34

That’s the exact answer. Since 34 is not a perfect square, we leave it as √34 unless told to approximate.

But let’s check — maybe they want a decimal? The worksheet doesn’t say, but since all problems are identical, and no rounding instructions are given, we’ll go with the exact value.

Wait — actually, looking again at the worksheet, each problem has a yellow box for the answer. It might expect a simplified radical or decimal. But √34 cannot be simplified further.

Alternatively, sometimes students are taught to write it as a decimal rounded to nearest tenth. Let’s calculate that too just in case.

√34 ≈ 5.83095... → rounds to 5.8 if to nearest tenth.

But since the original problem didn’t specify, and math worksheets often prefer exact answers unless stated otherwise, I think √34 is correct.

However — wait! Let me double-check my calculation.

Points: (8,8) and (3,5)

Δx = 3 - 8 = -5 → squared = 25
Δy = 5 - 8 = -3 → squared = 9
Sum = 34
√34 — yes, correct.

So final answer is √34.

But hold on — maybe the worksheet expects you to write the number only? Or perhaps they made a typo and meant different points? No, all six problems are exactly the same: “Distance between the points (8, 8) and (3, 5)”

So every answer should be the same: √34

But let me see — maybe they want it written as a decimal? In many middle school worksheets, they do ask for decimal approximations.

Let me compute √34 more precisely:

5.8² = 33.64
5.83² = 33.9889
5.831² = 34.000561 → very close!

So √34 ≈ 5.83

If rounding to nearest hundredth: 5.83
If to nearest tenth: 5.8

Since the worksheet says “show your work” and doesn’t specify, I think safest is to give exact value: √34

But let me check online or standard practice — actually, in most cases like this, especially if it's from mathbook.net, they may expect the simplified radical form.

Alternatively, maybe I misread the points? Let me re-read: “(8, 8) and (3, 5)” — yes.

Another thought: maybe they want the answer without the square root symbol? Like just the number under? No, that wouldn't make sense.

Or perhaps they want the full expression? Unlikely.

I think √34 is correct.

But to match what a student would write in the blank, probably just “√34” or “approximately 5.8”.

Looking at the layout — there’s an equals sign and then a yellow box. So likely they expect a number.

In many such worksheets, they accept either exact or approximate, but since 34 isn’t a perfect square, and no instruction, I’ll go with exact.

Final decision: Answer is √34

But let me confirm once more with actual calculation:

Distance = √[(8-3)^2 + (8-5)^2] = √[5^2 + 3^2] = √[25+9] = √34 — yes.

Note: I used (8-3) instead of (3-8), but since we square it, (-5)^2 = 25 same as 5^2. So order doesn’t matter.

So all good.

Final Answer: √34

But wait — the worksheet has six identical problems. Maybe it’s a trick? Or maybe it’s testing if you notice they’re all the same? Either way, answer is same for all.

So for each one, answer is √34.

But perhaps they want decimal? Let me see common core standards — usually in 8th grade, they teach distance formula and accept exact values.

I think √34 is fine.

Alternatively, maybe I should write it as a mixed number or something? No.

Okay, I’m confident.

Final Answer: √34