a Which school is approximately right in between the distance between the hospitals?
B
b Where are the museum and the schools located on their respective blocks?
A
a Roosevelt School
Explanation: See solution.
B
b No
Explanation: See solution.
Practice makes perfect
a
If we draw segments from the two hospitals to each of the schools, we see that the segments between the hospitals and the Roosevelt school looks like they are about the same length. Hence, they are approximately equidistant.
Note that the hospitals are both on Main street so if we draw a horizontal line through Mercy Hospital, it will also intercept the location of Trinity Hospital. Therefore, a vertical line through the Roosevelt School will be perpendicular to the horizontal line through the hospitals.
The reason why we know the Roosevelt school is approximately equidistant from the two hospitals is because it's horizontally almost right in between them.
Using the Perpendicular Bisector Theorem, we can claim that the Roosevelt school is almost equidistant from the endpoints of the segment between the hospital.
b Note that the museum, and the two schools are not in the middle of the blocks just because their labels take up the total width of the block. If they were, the location of the museum would be equidistant from the two schools.
However, the museum is on the right corner of its block and the schools are on the left side of their respective blocks.
Therefore, the museum is not approximately equidistant from Wilson school and Roosevelt School.
