Question

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

Home(0,4) 3rd(-4,0) 2nd(0,4) 1st(4,0)

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

(1 point)
Responses

22–√
2 square root of 2

42–√
4 square root of 2

4
4

-4
-4

Answer 1

To calculate the distance between first base (4, 0) and home plate (0, 4), we can use the distance formula:

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

Here, \( (x_1, y_1) \) is the coordinate of first base (4, 0) and \( (x_2, y_2) \) is the coordinate of home (0, 4).

Substituting the coordinates into the formula:

\[
d = \sqrt{(0 - 4)^2 + (4 - 0)^2}
\]
\[
= \sqrt{(-4)^2 + (4)^2}
\]
\[
= \sqrt{16 + 16}
\]
\[
= \sqrt{32}
\]
\[
= \sqrt{16 \cdot 2} = 4\sqrt{2}
\]

The shortest approximate unit distance from first base to home is \( 4\sqrt{2} \).

Thus, the correct answer is:

**4√2**