Question 498438: Mr Wong left his house and drove north for 5 blocks, then turned right and drove 6 blocks, then turned south and drove 2 more blocks. Finally, he turned right again and drove one more block to end up at the library.
How many blocks east of Mr Wong's house is the library ??
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Mr Wong is traveling in two basic directions (One direction is North-South and the other direction is East-West.)
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Since North-South is one line, let's call North moving in the + direction, and therefore South is in the opposite or - direction. (Think in terms of the X-Y coordinate axes. This can be compared to moving in the directions of the vertical or Y-axis.)
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And similarly East-West is one line. Let's say that East is in the + direction and West is in the opposite or - direction. (Again think in terms of the X-Y coordinate axes. This compares to moving in the directions of the horizontal or X-axes.)
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Let's now assume that Mr Wong's house is located at the origin of our coordinate system. (That it is located at (0,0)).
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To reach the library, Mr Wong first drives 5 blocks north. That would move him up the Y-axis 5 units to the (X,Y) point (0,5). Then he turns right and moves horizontally 6 blocks (in the east or +X direction). At the end of this leg he is now at the point (6,5). He turns right which means that he is now traveling south or in the negative Y direction and he goes for 2 blocks. So the Y value of the point is 2 less than it was and he arrives at the point (6,3). Finally, he turns right again and is now traveling horizontally to the left on our coordinate axes. This is the negative X direction, and since he goes 1 block to the library he reduces the X value by 1 and arrives at the point (5,3).
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Since both the X and Y values of this point are positive, we can tell that Mr Wong is both East and North of his house. The X value of the point tells us that he is 5 blocks East of his house. (That's the answer to this problem.) And also the Y value of this point tells us that he is 3 blocks North of his house.
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The straight line distance from his house to the library can be found by applying the distance formula (or Pythagorean theorem) to the right triangle formed by the origin (0,0) and the point (5,3). This triangle has legs of 5 and 3 and the straight line distance is the square root of the quantity 5^2 + 3^2.
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Hope this way of doing this problem isn't too confusing. Study it carefully. Using the system of coordinate axes to solve this problem reinforces a way of thinking that will become a useful tool in other areas such as the study of forces in physics.
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