To determine the shortest distance from first base to home in a baseball diamond drawn on a coordinate plane, we can assume the layout of the bases forms a square.
In a standard baseball diamond layout:
- Home base: (0, 0)
- First base: (90, 0)
- Second base: (90, 90)
- Third base: (0, 90)
Thus, the coordinates of first base are (90, 0) and home base is (0, 0).
We can calculate the distance between the two points using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates of first base and home:
\[ d = \sqrt{(0 - 90)^2 + (0 - 0)^2} = \sqrt{(-90)^2 + 0} = \sqrt{8100} = 90 \]
However, we need to verify the options provided:
-4 -4
4 4
\( 2\sqrt{2} \)
\( 4\sqrt{2} \)
Since 90 does not appear in the answers, if we modify the distance calculation according to the provided distance types or ratios, it’s clear that none of these options can directly express a distance that is close to 90 or matches the unit base metric we were provided.
Based on previous baseball guidelines where distances between the bases can be represented as root or local dimensional weight formats, and since it’s a right-angle triangle approach, the closest appropriate option that can represent a distance from first base to home correctly in reduced format from 90, considering 90 is standard without scaling factors might be something like:
\[ 2\sqrt{2} \approx 2.83 , \text{or from a reduction} 4\sqrt{2} \approx 5.66, \]
but neither can match or transform mathematically to average yardage metrics here aligning broadly intuitively with around 90.
In conclusion, as per standard metrics with no direct given conversions, it looks like “4” as a shorter base angle cutout potentially might be the closest but under standard drawing it might simply boil back down projectively to a recalibration suggesting distances to analyze visually via scales hence prior mathematical interpretations revert us back to designate a local round to compute effectively instabilities here.
However, if it strictly boils down to options, “4” possibly stands as practical choice evaluating none can truly correlate down directly to 90 as a base representation.