Distance And Midpoint Word Problems Worksheet - Free Printable

Let’s solve each of the 5 problems one by one using the distance formula:

> Distance Formula:
> For two points $(x_1, y_1)$ and $(x_2, y_2)$, the distance between them is:
> $$
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

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Problem 1

> Julie’s house: $(-2, 5)$
> Jimmy’s house: $(6, -2)$
> Find direct path (distance) between them.

Apply distance formula:

$$
d = \sqrt{(6 - (-2))^2 + (-2 - 5)^2} = \sqrt{(8)^2 + (-7)^2} = \sqrt{64 + 49} = \sqrt{113}
$$

✔ Answer: $\boxed{\sqrt{113}}$ units (or approximately 10.63 units)

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Problem 2

> Riley’s: 6 miles west and 3 miles north → coordinates relative to concert: $(-6, 3)$
> Brown’s: 2 miles east and 4 miles south → coordinates relative to concert: $(2, -4)$
> How far apart do they live? → Distance between $(-6, 3)$ and $(2, -4)$

$$
d = \sqrt{(2 - (-6))^2 + (-4 - 3)^2} = \sqrt{(8)^2 + (-7)^2} = \sqrt{64 + 49} = \sqrt{113}
$$

✔ Answer: $\boxed{\sqrt{113}}$ miles (≈ 10.63 miles)

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Problem 3

> Enemy patrol: 7 miles east and 11 miles north → $(7, 11)$
> Helicopter: 1 mile east and 3 miles north → $(1, 3)$
> Shortest distance helicopter can travel to enemy patrol → distance between $(1, 3)$ and $(7, 11)$

$$
d = \sqrt{(7 - 1)^2 + (11 - 3)^2} = \sqrt{(6)^2 + (8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10
$$

✔ Answer: $\boxed{10}$ miles

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Problem 4

> Walt City: $(-1, -3)$
> Koshville: $(4, 9)$
> Train route along straight line → distance between them

$$
d = \sqrt{(4 - (-1))^2 + (9 - (-3))^2} = \sqrt{(5)^2 + (12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13
$$

✔ Answer: $\boxed{13}$ miles

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Problem 5

> Kaleem: $(1, 3)$
> Jeremy: $(-6, 3)$
> Distance of pass in yards → note: same y-coordinate → horizontal line!

$$
d = \sqrt{(-6 - 1)^2 + (3 - 3)^2} = \sqrt{(-7)^2 + 0^2} = \sqrt{49} = 7
$$

Since it's a football field, and the problem asks for yards, and no unit conversion is given, we assume 1 unit = 1 yard.

✔ Answer: $\boxed{7}$ yards

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## ✔ Final Answers:

1. $\boxed{\sqrt{113}}$ units
2. $\boxed{\sqrt{113}}$ miles
3. $\boxed{10}$ miles
4. $\boxed{13}$ miles
5. $\boxed{7}$ yards

Let me know if you’d like diagrams or step-by-step graphs for any of these!