SOLUTION: My problem is regarding the distance and the midpoint which I do not know if Geometry or Algebra.The problem says, You and a friend go hiking. You hike 3 miles north and 2 miles

Algebra ->  Algebra  -> Length-and-distance -> SOLUTION: My problem is regarding the distance and the midpoint which I do not know if Geometry or Algebra.The problem says, You and a friend go hiking. You hike 3 miles north and 2 miles       Log On

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Question 198010This question is from textbook algebra 1 concepts and skills volume 2
: My problem is regarding the distance and the midpoint which I do not know if Geometry or Algebra.The problem says, You and a friend go hiking. You hike 3 miles north and 2 miles west. Starting from the same point, your friend hikes 4 miles east and 1 mile south.At the end of the hike how far apart are you and your friend?If you and your friend want to meet for lunch, where could you meet so that both of you hike the same distance?How far do you have to hike?I will really appreciate if you can help me with these problem. Many thanks.This question is from textbook algebra 1 concepts and skills volume 2

Answer by ankor@dixie-net.com(12701) About Me  (Show Source):
You can put this solution on YOUR website!
You hike 3 miles north and 2 miles west. Starting from the same point,
your friend hikes 4 miles east and 1 mile south.At the end of the hike.
how far apart are you and your friend?
:
Use graph paper. the Y axis is north/south, the x axis is east/west
Starting point is at the origin, 0,0
:
You hike to coordinates x1=-2, y1 =+3
your friend hikes to a point: x2=+4, y2 =-1
:
Use the distance equation: d =sqrt%28%28x1-x2%29%5E2+%2B+%28y2-y1%29%5E2%29
d =sqrt%28%284-%28-2%29%29%5E2+%2B+%28-1-3%29%5E2%29
:
d =sqrt%286%5E2+%2B+%28-4%29%5E2%29
:
d =sqrt%2836+%2B+16%29
:
d =sqrt%2852%29
d = 7.2 mi apart
:
:
If you and your friend want to meet for lunch, where could you meet so that
both of you hike the same distance?How far do you have to hike?
:
Use the mid-point equation: m.p. = %28x1%2Bx2%29%2F2, %28y1%2By2%29%2F2
:
mp = %28-2%2B4%29%2F2, %283-1%29%2F2
mp = 2%2F2, %282%29%2F2
mid-point: x = 1, y = 1
You would meet at coordinates: 1,1; which is 1 mi east and 1 mi north of the stating point.
Your drawing on the graph paper will confirm this.
:
You will each go half the distance: 7.2/2 = 3.6 mi
;
:
Did this all make sense to you? Let me know please.