Level of Difficulty E M
The diagram shows the path that Diane travels, but then asks how much shorter the trip would be if she went directly from A
. This distance is actually called the displacement, and is an important concept in physics
The distance she traveled on the path she chose was 16 + 15 + 4 = 35 miles. Now let's get the distance from A
. Then, we can take the difference between the two.
The key to getting the distance from A
is to form a large rectangle that contains the entire diagram, with the lower left corner of the rectangle at A
, and the upper right corner at D
. Now you will notice that the direct path we are interested in is the diagonal of the rectangle. This diagonal is also the hypotenuse of a right triangle whose legs have length 20 (16+4) and 15. We can apply Pythagorean's Theorem to find the length of the hypotenuse:
= 400 + 225
C = 25
Now we can answer the question "If she were able to travel from A
directly, how much shorter, in miles, would the trip be?" All we need to do is take the difference between the path she actually walked (35 miles) and the straight-line distance between A
(25 miles) which gives 10 miles, or choice C.
You might also have noticed that the legs of a right triangle with lengths 15 (3X5) and 20 (4X5) must be the legs of a 3-4-5 right triangle, so the hypotenuse must be 25 (5X5).
If you are interested in learning more about displacement, visit The Physics Classroom.
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