Hi reto,

Any time that you have a diagonal line segment on a graph, you can "build" a right triangle around it (using the diagonal as the hypotenuse of the triangle). In this way, you can use the Pythagorean Theorem to calculate the length of the line segment.

Here, we have the co-ordinates (1, 1) and (1.5, 1.5). Drawing a right triangle here would give us a base of .5 and a height of .5

Using the Pythagorean Theorem, we have...

A^2 + B^2 = C^2

(.5)^2 + (.5)^2 = C^2

.25 + .25 = C^2

.5 = C^2

From here, you have to do a little work to "clean up" the answer

1/2 = C^2

Root(1/2) = C

Root(1/2) = (Root1)/(Root2) = 1/(Root2)

As a general rule, radicals in the denominator of a fraction are a "no-no", so you have to do the necessary math to 'get rid' of any radicals in the denominator.....

With 1/(Root2), we can multiply both the numerator and denominator by (Root2). This gives us...

(Root2)/[(Root2)^2] = (Root2)/2

Final Answer:

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Rich

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