The grid below shows three towns in the same county. Distances in the grid are in miles.

Question

Portlock is at (-6, 6), Bernwood is at (8, 6), Cedar cove is at (8, -4).

What is the shortest distance, in miles, between Porlock and Cedar Cove? Round your answer to the nearest tenth, if necessary.

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_____ Miles

Answer 1

To find the shortest distance between Portlock and Cedar Cove, we can use the distance formula, which is given by:

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

Here, we have the coordinates for Portlock at (-6, 6) and Cedar Cove at (8, -4). Plugging these coordinates into the distance formula:

• \(x_1 = -6\), \(y_1 = 6\)
• \(x_2 = 8\), \(y_2 = -4\)

Now calculating:

\[ d = \sqrt{(8 - (-6))^2 + (-4 - 6)^2} \]

First, simplify the expressions inside the parentheses:

\[ d = \sqrt{(8 + 6)^2 + (-4 - 6)^2} \] \[ = \sqrt{(14)^2 + (-10)^2} \] \[ = \sqrt{196 + 100} \] \[ = \sqrt{296} \]

Next, we can find the approximate value of \(\sqrt{296}\):

\[ \sqrt{296} \approx 17.2 \]

Thus, the shortest distance between Portlock and Cedar Cove is approximately \(17.2\) miles when rounded to the nearest tenth.

So, the final answer is:

\[ \boxed{17.2} \text{ miles} \]