Question 1207834: Rewrite the statement using absolute value notation.
The sum of the distances of a and b from the origin is greater than or equal to the distance of a + b from the origin.
Answer by ikleyn(52832)   (Show Source):
You can put this solution on YOUR website! .
Rewrite the statement using absolute value notation.
The sum of the distances of a and b from the origin is greater
than or equal to the distance of a + b from the origin.
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I don't know, at what scene the action of this play takes place: in the number line,
or in a plane (2D), or in space (3D). But I will tell the story, assuming that the play is on a plane (2D).
|a| + |b| >= |a+b|. ANSWER
Explanation
On the plane, we have the origin O;
point A at the distance "a" from O (represents vector OA of the length "a");
point B at the distance "b" from O (represents vector OB of the length "b").
In this interpretation, a+b is the third side of the triangle OAB (the parallelogram rule of adding vectors).
Then the triangle inequality says that
|a| + |b| >= |a+b|.
It is precisely what they want you prove.
Solved.
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