The grid below shows different locations in Henry’s town. Each unit represents 1 mile.

Question

The post office is at (2, 16), the library is at (2, 4), and the store is at (negative 8, 4).

What is the distance, in miles, between the Post Office and the Store? Round your answer to the nearest tenth, if necessary.

Type your response in the box below.

Math Equation Response Question
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miles

Answer 1

To find the distance between the Post Office at (2, 16) and the Store at (-8, 4), we can use the distance formula, which is given by:

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

Here, \((x_1, y_1) = (2, 16)\) and \((x_2, y_2) = (-8, 4)\).

Substituting the coordinates into the formula:

\[ d = \sqrt{((-8) - 2)^2 + (4 - 16)^2} \] \[ = \sqrt{(-10)^2 + (-12)^2} \] \[ = \sqrt{100 + 144} \] \[ = \sqrt{244} \]

Now we can calculate \(\sqrt{244}\):

\[ \sqrt{244} \approx 15.6205 \]

Rounding to the nearest tenth:

\[ \sqrt{244} \approx 15.6 \]

Thus, the distance between the Post Office and the Store is approximately:

15.6 miles.