Quizizz worksheet featuring 10 questions on the distance formula, testing understanding of its correct application.

Let's go through each question step by step and solve them using the distance formula.

---

🔷 Distance Formula:

The distance $ d $ between two points $ A(x_1, y_1) $ and $ B(x_2, y_2) $ is:

$$
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

This is the correct form. It uses squares of differences, summed, then square root taken.

---

✔ Question 1:

How is the distance formula correctly written?

We are to pick the correct version of the formula.

- A: $ d = \sqrt{(y_1 - y_2)^2 + (x_2 - x_1)^2} $ → Correct order, but variables switched — still mathematically equivalent.
- B: $ d = \sqrt{(x)^2 - (y)^2} $ → Wrong, missing subscripts and structure.
- C: $ d = \sqrt{(y_1 - y_2)^2 - (x_2 - x_1)^2} $ → Minus sign instead of plus → wrong.
- D: $ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $ → ✔️ This matches the standard formula.

✔ Answer: D

> Note: A is also algebraically correct since $ (y_1 - y_2)^2 = (y_2 - y_1)^2 $, but D is the standard format.

But since D is the conventional way, D is best choice.

---

✔ Question 2:

Points: $ A(3,1) $, $ B(-2,-1) $

Use:
$$
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

Let’s plug in:
- $ x_1 = 3 $, $ y_1 = 1 $
- $ x_2 = -2 $, $ y_2 = -1 $

So:
$$
d = \sqrt{(-2 - 3)^2 + (-1 - 1)^2} = \sqrt{(-5)^2 + (-2)^2}
$$

Now check options:

- A: $ \sqrt{(-2 - 3)^2 - (-1 - 1)^2} $ → minus sign ✘
- B: $ \sqrt{(-2 - 3)^2 + (-1 - 1)^2} $ → ✔️ Correct
- C: $ \sqrt{(1 - 3)^2 + (-1 - 2)^2} $ → wrong coordinates
- D: $ \sqrt{(-2 - 3)^2 - (-1 - 1)^2} $ → minus again ✘

✔ Answer: B

---

✔ Question 3:

Points: $ A(5,1) $, $ B(-2,6) $

Using:
$$
d = \sqrt{(-2 - 5)^2 + (6 - 1)^2} = \sqrt{(-7)^2 + (5)^2}
$$

Check options:

- A: $ \sqrt{(1 - 5)^2 + (6 - 2)^2} $ → wrong x-values ✘
- B: $ \sqrt{(-2 - 5)^2 - (6 - 1)^2} $ → minus ✘
- C: $ \sqrt{(-2 - 5)^2 - (6 - 1)^2} $ → same error ✘
- D: $ \sqrt{(-2 - 5)^2 + (6 - 1)^2} $ → ✔️ Correct

✔ Answer: D

---

✔ Question 4:

Points: $ R(7, -2) $, $ Q(-3, 5) $

$$
d = \sqrt{(-3 - 7)^2 + (5 - (-2))^2} = \sqrt{(-10)^2 + (7)^2}
$$

Now check options:

- A: $ \sqrt{(-3 - 7)^2 + (5 + 2)^2} $ → $ (5 + 2) = 7 $, so yes! ✔️
- B: $ \sqrt{(5 + 3)^2 - (-2 - 7)^2} $ → subtraction and wrong values ✘
- C: $ \sqrt{(-3 - 7)^2 - (5 - 2)^2} $ → minus ✘
- D: $ \sqrt{(7 + 2)^2 + (-3 - 5)^2} $ → wrong signs and values ✘

✔ Answer: A

---

✔ Question 5:

Points: $ K(1,2) $, $ L(9,5) $

$$
d = \sqrt{(9 - 1)^2 + (5 - 2)^2} = \sqrt{8^2 + 3^2}
$$

Check options:

- A: $ \sqrt{(9 - 5)^2 + (2 - 1)^2} $ → wrong coordinates ✘
- B: $ \sqrt{(9 - 1)^2 + (5 - 2)^2} $ → ✔️ Correct
- C: $ \sqrt{(9 - 2)^2 - (5 - 1)^2} $ → minus and wrong values ✘
- D: $ \sqrt{(9 - 5)^2 - (2 - 1)^2} $ → minus and wrong ✘

✔ Answer: B

---

✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | D |
| 2 | B |
| 3 | D |
| 4 | A |
| 5 | B |

---

Let me know if you'd like the actual numerical distances calculated too!