## Capture the Flag!

The Algebra and Geometry classes at Mathland Hgh School are planning to play a game of Capture the Flag in the woods behind the school. They’ve been discussing how to fairly divide the woods into two territories.

They’ve drawn a map of the woods and added a coordinate plane. The Algebra class will put their base at (-8, 15). The Geometry class will put their base at (4, -3).

Find the line which pass thru the bases

Find the midpoint of line

Find the prependicular bisector

A will have the area above the line

B will have the area below the line

Hi Frankie,

I can totally follow your method and I would definitely consider it for dividing the area fairly.

One thing I wondered is, does it divide the woods into two equal areas, even though the woods are kind of lumpy?

Would your method always work for any shaped woods?

Thanks for commenting!

Max

One thing that I noticed is it seems that Base A seems to be slightly closer to the edge of the boundaries. I wonder if we can prove this mathematically and figure out if one of the bases has more or less room to work with.

I noticed that the Algebra and Geometry classes want to play capture the flag and need to divide the woods behind their school evenly into two territories. On the map of the woods, the Algebra class will put their base at (-8, 15) and the Geometry class will put theirs at (4, -3). I wonder why they didn’t make the coordinate plane more centered when they drew the map? I wonder if the territory really will be evenly divided if they put their bases on (-8, 15) and (4, -3)? Can the territory even be divided evenly? Can it be proven mathematically?

Wait so what would the equation be?

Hi, Alexis. That answer depends. What are you thinking the equation would represent? What question is it that you’re trying to answer?