I have an angled line from x1,y1 to x2,y2.  From the x and y
differences, I can derive a right triangle, and then with the
pythagorean theorem, get the length of the line.

Now, I have to shorten the line to a random length between 0 and it's
original length, keeping the angle the same and keeping x1,y1 the
same.  How do I determine the coordinates of the new x2,y2.

Something I can easily translate into Perl would be useful.

I'm currently searching for the answer, so answer fast.

Hi bongobud,

We can calculate this using the theorem that the corresponding sides
of similar triangles are proportional.

Let's start with a few definitions.

Let e1 be the distance between (x1, y1) and (x2, y2).

Let e2 be the shortened distance.

Let (x3, y3) be the coordinates you seek, the other end of the
shortened line from (x1, y1).

The length of the horizontal side of the original triangle is (x2 -
x1).  The proportion of shortening is (e2 / e1).  So according to the
theorem, the length of the horizontal side of the reduced triangle is
((x2 - x1) * (e2 / e1)).  x3 is located this length past x1, so x3 =
x1 + ((x2 - x1) * (e2 / e1)).

Similarly, the length of the vertical side of the original triangle is
(y2 - y1), the length of the vertical side of the reduced triangle is
((y2 - y1) * (e2 / e1)), and y3 = y1 + ((y2 - y1) * (e2 / e1)).


Additional Links

A few pages that state that the corresponding sides of similar
triangles are proportional:

Euclid's Elements, Book VI, Proposition 19
http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/propVI19.html

Similar triangles on everything2.com
http://www.everything2.com/index.pl?node=Similar%20triangles

Tim's Triangular Page
http://sakharov.net/triangle.html


This should be reasonably easy to code in Perl.  If you need any more
help with this, please feel free to ask for a clarification.

Regards,

--efn

Expressed in overly complex.  Could have been described in a couple of
quick sentences.

shame on you, efn, for wasting bongobud's valuable time like that.

-cab

Well Bongobud, if the answer could have been expressed in a couple of
quick sentences, perhaps you should have done so and saved yourself $5

I count 11 sentences not including the links totalling 105 words. Two
sentences (22 words) are introductory and three (25 words) are
definition.

So there are six sentences containing 58 words (plus math expressions)
to answer your question. If we remove all instances of "the," and the
one each of "so," and "similarly," meaning is not lost and the word
count drops by 15 to 43 words.

Is this the overly complex expressing to which you refer, Bongobud?

I'm thinking someone didn't understand the rather brilliant way the
question was answered.

Perhaps he should not have asked a question he was not able to
comprehend the answer to.

usrhlp