Question

each unit on a coordinate plane is equivalent to 0.5 miles Alex's house is located at (-5, -4) and the library is located at (-5, 3) how far in miles is Alex's house from the library

Answer 1

To find the distance between Alex's house at the coordinates \((-5, -4)\) and the library at \((-5, 3)\) on a coordinate plane, we can use the distance formula for points:

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

In this case:
- \(x_1 = -5\), \(y_1 = -4\) (Alex's house)
- \(x_2 = -5\), \(y_2 = 3\) (library)

Now, plug the coordinates into the formula:

\[
d = \sqrt{(-5 - -5)^2 + (3 - -4)^2}
\]
\[
d = \sqrt{(0)^2 + (3 + 4)^2}
\]
\[
d = \sqrt{0 + 7^2}
\]
\[
d = \sqrt{49}
\]
\[
d = 7
\]

Since each unit is equivalent to 0.5 miles, we convert the distance from units to miles:

\[
\text{Distance in miles} = 7 \times 0.5 = 3.5
\]

Therefore, the distance from Alex's house to the library is \(3.5\) miles.