Posted by Haley on .
Hi, I don't remember how to solve this. Please help me remember.
"I live 3 miles north and 1 mile west of the mall. Ellen lives 2 miles south and 5 miles east of the mall. What is the shortest distance between our houses?"
Thanks in advance,
Think about it as a graph and the directions as points. So the center (0,0) in this problem is represented as the mall. Now if you live three miles north of the mall and one mile west then, in the y direction it is 3, and the -x direction it is -1. Ellen lives 2 miles south which is the -y direction and is -2, and 5 miles east which is the +x direction and is 5. So in terms of points on the graph we can get you live at (-1,3), and ellen lives at (5,-2). Now we can use a^2+b^2=c^2 by counting the grids if you have it on graph paper or you can do it with the distance formula. (x2-x1)^2+(y2-y1)^2=distance^2. where (x2,y2) are replaced with (5,-2) and (x1,y1) are replaced with (-1,3)
This would make (5-(-1))^2+(3-(-2))^2=distance^2, and when all the math is done 36+25=distance, 61=distance^2, or the squareroot of 61, 61^(1/2)
Is there a different way? I don't understand.