Unit 1 Geometry Basics | PDF - Free Printable

Since the user has set all options (ExplainAnswer, TeachTopic, GeneratePractice) to false, I will only provide the final answers for each problem on the worksheet.

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Problem 1:
Points: (-4, 6) and (3, -7)
Distance = √[(3 - (-4))² + (-7 - 6)²] = √[7² + (-13)²] = √[49 + 169] = √218 ≈ 14.8

Problem 2:
Points: (-6, -5) and (2, 0)
Distance = √[(2 - (-6))² + (0 - (-5))²] = √[8² + 5²] = √[64 + 25] = √89 ≈ 9.4

Problem 3:
Points: (-1, 4) and (1, -1)
Distance = √[(1 - (-1))² + (-1 - 4)²] = √[2² + (-5)²] = √[4 + 25] = √29 ≈ 5.4

Problem 4:
Points: (0, -8) and (3, 2)
Distance = √[(3 - 0)² + (2 - (-8))²] = √[3² + 10²] = √[9 + 100] = √109 ≈ 10.4

Problem 5:
From graph: Points are approximately (-6, -2) and (2, 7)
Distance = √[(2 - (-6))² + (7 - (-2))²] = √[8² + 9²] = √[64 + 81] = √145 ≈ 12.0

Problem 6:
Endpoints: A(5, 8) and B(-1, -4)
Midpoint x = (5 + (-1))/2 = 4/2 = 2
Midpoint y = (8 + (-4))/2 = 4/2 = 2 → Wait, correction:
Actually, (5 + (-1)) / 2 = 4/2 = 2? No — wait, let’s recalculate:

Wait — original handwritten answer says (3, 6). Let me check:

A(5,8), B(-1,-4)

x: (5 + (-1)) / 2 = 4/2 = 2
y: (8 + (-4)) / 2 = 4/2 = 2 → That gives (2,2), but that doesn’t match the student’s work.

Wait — perhaps I misread the points? Student wrote: (5+(-1))/2 and (8+(-4))/2 → which is (4/2, 4/2) = (2,2). But they wrote (3,6)? That must be a mistake.

Wait — looking again at student’s work: They wrote “(5 + (-1))/2” and “(8 + (-4))/2”, then simplified to (4/2, 4/2) = (2,2), but then wrote (3,6)? That seems like an error.

But actually — maybe the points are different? Let me recheck the image description.

In the image, Problem 6: A(5,8) and B(-1,-4)

Correct midpoint: ((5 + (-1))/2, (8 + (-4))/2) = (4/2, 4/2) = (2, 2)

But student wrote (3,6) — that’s incorrect. However, since we’re solving accurately, we give correct answer.

Wait — perhaps I made a mistake? Let me double-check:

x-coordinate: (5 + (-1)) ÷ 2 = 4 ÷ 2 = 2
y-coordinate: (8 + (-4)) ÷ 2 = 4 ÷ 2 = 2
→ Midpoint is (2, 2)

But student’s handwriting shows (3,6) — likely a calculation error. We’ll go with correct math.

However — wait! Looking back at the student’s work in the image: They wrote “(5 + (-1))/2” and “(8 + (-4))/2”, then underlined and wrote (3,6)? That doesn’t add up. Perhaps they meant something else?

Actually — no, let’s trust the math. Correct answer is (2,2).

But hold on — maybe the points are A(5,8) and B(-1,4)? No, it says B(-1,-4).

I think there’s a typo in my reading or the student’s work. To resolve:

Let me calculate again:

A(5,8), B(-1,-4)

Midpoint formula: ((x₁+x₂)/2, (y₁+y₂)/2)

x: (5 + (-1)) / 2 = 4/2 = 2
y: (8 + (-4)) / 2 = 4/2 = 2
→ (2,2)

But student wrote (3,6) — probably wrong. Since we’re providing accurate solution, we use (2,2).

Wait — perhaps the point is B(-1,4)? Then y would be (8+4)/2=6, and x=(5-1)/2=2 → still not 3.

If A(5,8) and B(1,-4): x=(5+1)/2=3, y=(8-4)/2=2 → (3,2) — not 6.

If A(5,8) and B(1,4): x=3, y=6 → ah! Maybe the point is B(1,4)? But the text says B(-1,-4).

Given the confusion, I’ll stick to what’s written: A(5,8), B(-1,-4) → midpoint (2,2)

But let’s look at Problem 7 for comparison.

Problem 7: M(-5,9), N(-2,7)

Student wrote: (-5 + (-2))/2 = -7/2 = -3.5, (9+7)/2=16/2=8? But they wrote 1? Wait, they have ( -3.5, 1 ) — that can’t be right.

(9+7)/2 = 16/2 = 8, not 1. So student made error.

Similarly, Problem 8: P(-3,-7), Q(3,-5)

Midpoint: x=(-3+3)/2=0/2=0, y=(-7 + (-5))/2 = -12/2 = -6 → (0,-6)

But student wrote (-3,-1) — incorrect.

Problem 9: F(2,-6), G(-8,5)

Midpoint: x=(2 + (-8))/2 = -6/2 = -3, y=(-6 + 5)/2 = -1/2 = -0.5 → (-3, -0.5)

Student wrote (1, -5.5) — incorrect.

So many errors in student’s work. As an educational assistant, I should provide correct answers.

Therefore, for accuracy:

Final Answers:

1. 14.8
2. 9.4
3. 5.4
4. 10.4
5. 12.0
6. (2, 2)
7. (-3.5, 8)
8. (0, -6)
9. (-3, -0.5)

But wait — for Problem 5, the student calculated √145 ≈ 12.04, so 12.0 is fine.

For Problem 6, if we follow strict math, it's (2,2). But let me confirm once more.

Perhaps the point is B(-1,4)? Then y=(8+4)/2=6, x=(5-1)/2=2 → (2,6) — still not (3,6).

If A(5,8) and B(1,4): x=3, y=6 → (3,6). So maybe it's a typo in the problem or student misread.

Given that the student got (3,6), and it's common to have such typos, but as AI, I must solve based on given numbers.

The problem states: "A(5,8) and B(-1,-4)" — so I'll use that.

Thus, corrected answers:

6. (2, 2)
7. (-3.5, 8)
8. (0, -6)
9. (-3, -0.5)

But to match typical expectations, let's write them clearly.

Also, for distances, they rounded to one decimal place, so we do same.

Now, compiling final answers as per instruction.

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Final Answer:
1. 14.8
2. 9.4
3. 5.4
4. 10.4
5. 12.0
6. (2, 2)
7. (-3.5, 8)
8. (0, -6)
9. (-3, -0.5)