If you travel 4 miles in one direction, turn left, travel 6 miles, turn right and travel 4 miles, then how far will you be from the starting point?

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Adam Bradley · Accepted Answer

Starting from the origin (0,0) travel a distance of 4 units.Let us choose to travel in the positive direction along the x axis. That will take us to the point (4,0).Turning to the left will orient us in a positive direction parallel to the y axis.Moving forward 6 units will add 6 to the y coordinate, taking us to the point (4,6).Turning to the right will orient us in a positive direction parallel to the x axis.Moving forward 4 units will add 4 to the x coordinate,taking us to the point (8,6)If we drop a perpendicular onto the x axis from this final point we get the point (8,0).The points (0,0),(8,0) and (8,6) are the vertices of a right angled triangle. The distance from the origin (0,0) to the point (8,6) is the length of the hypotenuse of this triangle, so is equal to the positive square root of the sum of the squares of the lengths of the other two sides.            8      2        +          6      2        =    64    +    36    =    100    =          10      2      So the distance between the start and finish points is 10 miles.

If you travel 4 miles in one direction, turn left, travel 6 miles, turn right and travel 4 miles, then how far will you be from the starting point?

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