Question

Gabriella draws a scale drawing of a baseball diamond on the coordinate plane below.The angle at each base is a right angle.

The coordinate plane shows a square with edges labeled first at (4, 0), second at (0, 4), third at (-4, 0) and Home at (0, -4).

In her drawing, what is the shortest approximate unit distance from first base to home?

Answer 1

To find the distance from first base at the point (4, 0) to home at (0, -4), we can use the distance formula, which is given by:

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

In this scenario, we have:
- \( (x_1, y_1) = (4, 0) \) (coordinates of first base)
- \( (x_2, y_2) = (0, -4) \) (coordinates of home)

Plugging in these values into the distance formula:

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

Calculating the differences:

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

Squaring the terms:

\[
d = \sqrt{16 + 16}
\]

Adding them together:

\[
d = \sqrt{32}
\]

This can be simplified further:

\[
d = \sqrt{16 \times 2} = 4\sqrt{2}
\]

To provide an approximate decimal value for the distance, we can calculate \( \sqrt{2} \) which is approximately 1.414. Thus:

\[
d \approx 4 \times 1.414 = 5.656
\]

Therefore, the shortest approximate unit distance from first base to home is:

\[
\boxed{5.656}
\]