Distance And Midpoint Word Problems Worksheet - Free Printable

Since I can't view or access uploaded images directly, I can’t see the specific image you're referring to. However, based on your message, it appears that you've provided a list of distance and midpoint word problems in text form — likely from a worksheet.

Let me solve each problem step by step, assuming the problems are as written below:

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Problem 1:

On a map, Julie's house is located at (–2, –5), and Jimmy's house is at (6, –5). How long is the direct path from Julie’s house to Jimmy’s house?

#### Solution:
We use the distance formula:
$$
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

Given:
- Julie: $(-2, -5)$
- Jimmy: $(6, -5)$

$$
d = \sqrt{(6 - (-2))^2 + (-5 - (-5))^2} = \sqrt{(8)^2 + (0)^2} = \sqrt{64} = 8
$$

✔ Answer: The direct path is 8 units long.

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Problem 2:

The Riley and Brown families decided to go to a concert together. The Riley’s live 6 miles west and 3 miles south of the concert. The Browns live 2 miles east and 4 miles south. How far apart are they?

#### Step 1: Assign coordinates
Let the concert location be the origin: $(0, 0)$

- Riley’s home: 6 miles west → $x = -6$, 3 miles south → $y = -3$ → $(-6, -3)$
- Brown’s home: 2 miles east → $x = 2$, 4 miles south → $y = -4$ → $(2, -4)$

#### Step 2: Use distance formula
$$
d = \sqrt{(2 - (-6))^2 + (-4 - (-3))^2} = \sqrt{(8)^2 + (-1)^2} = \sqrt{64 + 1} = \sqrt{65}
$$

✔ Answer: They are $\sqrt{65}$ miles apart ≈ 8.06 miles.

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Problem 3:

A command center learns that an enemy patrol is located 7 miles east and 13 miles north of their position. If the command center's helicopter is located 1 mile east and 2 miles north of the center, what is the shortest distance the helicopter can travel to get to the enemy patrol?

#### Step 1: Assign coordinates
Let the command center be at $(0, 0)$

- Enemy patrol: 7 miles east, 13 miles north → $(7, 13)$
- Helicopter: 1 mile east, 2 miles north → $(1, 2)$

#### Step 2: Distance between helicopter and enemy patrol
$$
d = \sqrt{(7 - 1)^2 + (13 - 2)^2} = \sqrt{6^2 + 11^2} = \sqrt{36 + 121} = \sqrt{157}
$$

✔ Answer: The shortest distance is $\sqrt{157}$ miles ≈ 12.53 miles.

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Problem 4:

On a map's coordinate grid, Wall City is located at (–1, –3) and Rushville is located at (4, 9). How long is the route if a train travels along a straight line from Wall City to Rushville? (One map unit equals one mile.)

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

✔ Answer: The route is 13 miles long.

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Problem 5:

Coach Avarado places his football team’s end zone on the coordinate plane. He placed Kaiten at (2, 13), and Jeremy at (–6, 3). What is the distance, in yards, of the path from Kaiten to Jeremy?

Assuming the coordinate units represent yards, use distance formula:

$$
d = \sqrt{(-6 - 2)^2 + (3 - 13)^2} = \sqrt{(-8)^2 + (-10)^2} = \sqrt{64 + 100} = \sqrt{164}
$$

Simplify:
$$
\sqrt{164} = \sqrt{4 \cdot 41} = 2\sqrt{41} \approx 12.81 \text{ yards}
$$

✔ Answer: The distance is $2\sqrt{41}$ yards ≈ 12.81 yards.

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✔ Final Answers Summary:

1. 8 units
2. $\sqrt{65}$ miles ≈ 8.06 miles
3. $\sqrt{157}$ miles ≈ 12.53 miles
4. 13 miles
5. $2\sqrt{41}$ yards ≈ 12.81 yards

Let me know if you’d like these answers formatted differently or if you have any questions!