Increase length of line

Question

I have line segment from

Start Point ($x1$,$y1$) = (279,268) and End Point ($x2$,$y2$) = (281,198)

I want to increase the length of line by 5, 10, 20 etc in end point direction.

i.e value of $y2$ should decrease like 198 -> 193 -> 183 - 163 etc.

Is there any formula through which i can get new values of ($x2$,$y2$) by providing the increase in length constant c (5, 10, 20)?

Thanks

Eckhard · Accepted Answer · 2016-01-06T06:54:21.387

6

Compute $$ \Delta_x=\frac{x_2-x_1}{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}} $$ and $$ \Delta_y=\frac{y_2-y_1}{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}. $$

Then your new point has coordinates $$ (x_2+c\Delta_x, y_2+c\Delta_y). $$

edited Jan 06 '16 at 06:54

answered Apr 06 '13 at 10:00

Eckhard

7,705

I know this is an old answer, but shouldn't the equation be (y2 - y1)^2 not (y2 - y2)^2, which is 0? – Chris Stillwell Jan 05 '16 at 19:54
Edited, thanks @ChrisStillwell. – Eckhard Jan 06 '16 at 06:54

score 0 · Answer 2 · answered Apr 06 '13 at 10:01

0

The new endpoint is given by $$(x^\prime_2,y^\prime_2) = (x_2,y_2) + \frac{l}{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}(x_2-x_1,y_2-y_1) = (281+\frac{l\sqrt{1226}}{1226},198-\frac{35l\sqrt{1226}}{1226}),$$

where $l$ is the additional length of the line.

answered Apr 06 '13 at 10:01

Abel

7,312

Increase length of line

2 Answers2