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Question

Part 1
Use the map shown below to find the distance between cities A and B to the nearest tenth.
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Upper BUpper A

A graph with horizontal x-axis from negative 10 to 10 in increments of 1 and vertical y-axis from negative 10 to 10 in increments of 1 has the following labels and points: A, (0,0); B, (6, 3).
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Part 1
The distance is
  
enter your response here.
​(Round to the nearest tenth as​ needed.)

Answer 1

To find the distance between points A(0, 0) and B(6, 3), we can use the distance formula:

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

Here:

• \( (x_1, y_1) = (0, 0) \)
• \( (x_2, y_2) = (6, 3) \)

Plugging the coordinates into the formula:

\[ d = \sqrt{(6 - 0)^2 + (3 - 0)^2} \ d = \sqrt{(6)^2 + (3)^2} \ d = \sqrt{36 + 9} \ d = \sqrt{45} \]

Now, simplifying \(\sqrt{45}\):

\[ \sqrt{45} = \sqrt{9 \cdot 5} = 3\sqrt{5} \]

Using a calculator to approximate \(\sqrt{5}\) (which is about 2.236):

\[ 3\sqrt{5} \approx 3 \cdot 2.236 \approx 6.708 \]

Rounding to the nearest tenth gives us:

\[ \text{Distance} \approx 6.7 \]

So the distance between cities A and B is approximately 6.7.