Distance and Midpoint help

[dukjos21]

I do not know if this would be in geometry but I thought I would post it here. I really need help with this work worksheet because If I don't get it done I won't get credits for my class and my teacher can't help me right now.




These are the problems so pretty much I need to find two stores that would give me a midpoint that would fall in the region of the rectangle area I have made.

 

[Dr.Peterson]

I do not know if this would be in geometry but I thought I would post it here. I really need help with this work worksheet because If I don't get it done I won't get credits for my class and my teacher can't help me right now.

These are the problems so pretty much I need to find two stores that would give me a midpoint that would fall in the region of the rectangle area I have made.

Geometry fits fine. This is coordinate geometry, which falls into that category.

I would choose the two stores by eye: Just pick a store, pick a store that is across the open area from it, and check whether the point halfway between is inside the rectangle. If you aren't sure, use a ruler to measure the approximate distance between the two doorways (this won't be part of your actual answer), and measure halfway to find the midpoint. There are many possibilities, so if you have any sense of what a midpoint is, it shouldn't take many tries to find a pair that work. (If the store's doorway is required to have integer coordinates, it might take a couple more tries.)

Then you can do the actual calculation of the midpoint (using the midpoint formula) to state the answer.

Then show us your work and your answer, so we can check it out and offer any advice you might need.

 

[HallsofIvy]

It looks to me like your only difficulty is that there are a number of valid answers because you can measure from any point in a store to any point in that rectangle. Choose a store on one side, say the music store. The distance from some point in that store to some point inside the given rectangle is anything from \(\displaystyle \sqrt{5}\) to \(\displaystyle \sqrt{221}\) (about 15). You should be able to find another store that is one of those distances to the right and below.