Question 1083532
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Answer: <font color=red>100 meters</font>
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Note: this is a page edit. My last answer was incorrect. I realized I misread the problem. The solution has been corrected now.


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Explanation:


Let point A be at the origin. 
The origin is the point (0,0) which is where the x and y axis meet.
This is where the woman will start.


She walks 20 meters west, so she ends up at (-20,0) which is marked by point B.


Then she walks 100 meters south ending up at point C (-20,-100)


After that, she walks 8 meters west to get to D = (-28,-100). (This is where my initial error was made, but it has been fixed now. Point E has been updated as well)


Finally, she walks 4 meters north to end up at point E, which is located at (-28,-96)


Let's draw all this out
<img src="https://i.imgur.com/EwAR87J.png">
The coordinates of each point are
A = (0, 0)
B = (-20, 0)
C = (-20, -100)
D = (-28, -100)
E = (-28, -96)


The goal is to find the distance from A to E. 
This is the same as finding the length of segment AE (or segment EA).


We use the distance formula. The two points used are
(x1,y1) = (0,0) ... point A
(x2,y2) = (-28,-96) ... point E


So we have x1 = 0, y1 = 0, x2 = -28, and y2 = -96, which means:
{{{d = sqrt((x[2]-x[1])^2+(y[2]-y[1])^2)}}}


{{{d = sqrt((-28-0)^2+(-96-0)^2)}}} Plug in the values mentioned above


{{{d = sqrt((-28)^2+(-96)^2)}}}


{{{d = sqrt(784+9216)}}}


{{{d = sqrt(10000)}}}


{{{d = 100}}}


The exact distance is 100 meters.</font>