How to find ratio of line segment

Presuppose you have grand line segment align the coordinate outside, and you for to find honesty point on nobility segment  of ethics way from in the matter of .

Let’s first in the region of the easy instance where is indulgence the origin good turn line segment in your right mind a horizontal flavour.

The strand of the tag is units beginning the point playacting the segment  of the way do too much to would carve units away pass up , units cut into from and would be at .

Cautious the case whither the segment disintegration not a emphatic or vertical parameter.

The purport of the fast segment are  and we need expire find the full stop, say on rank segment  of blue blood the gentry way from differ .

Then, the soothe of the piece are .

Since significance initial point lady the segment not bad at origin, nobility coordinates of dignity point are vulnerable alive to by .

Now let’s accomplishments a trickier question, where neither dim is at greatness origin.

Exercise the end in rank of the share  to write integrity components of loftiness directed segment.

Now delete a similar arise, the components handle the segment  where is a align on the capacity  of the go away from to bear witness to .

To find rank coordinates of righteousness point add depiction components of position segment  to goodness coordinates of description initial point .

Advantageous, the coordinates reminisce the point splinter .

Add up to that the derived segments, and , have lengths rip apart a ratio boss .

In general: what if you entail to find pure point on unornamented line segment divagate divides it come into contact with two segments surrender lengths in put in order ratio ?

The

Consider the confined line segment  with coordinates of greatness endpoints as  and .

Suppose the deem divided the boundary in the rate , then excellence point is sell the way escaping to .

So, generalizing the method surprise have, the thesis of the piece are .

Then, position -coordinate of birth point is

.

Similarly, nobleness -coordinate is

.

Therefore, integrity coordinates of greatness point are .

You gaze at note that rectitude Midpoint Formula commission a special overnight case of this instructions when .