I have the coordinates of the endpoints of the line as $(x_1,y_1)$ and $(x_3,y_3)$. The difference in coordinate 'delta' refers to either $\Delta x$ or $\Delta y$ (We do not know which one it is) with respect to the first point $(x_1,y_1)$. However it is known that it is the larger difference i.e., Given $a>b$, if $x_2 = x_1+a$ and $y_2 = y_1+b$, then the 'delta' is $\Delta x$. Conversely, if $a<b$ and the other conditions remain the same, then the 'delta' is $\Delta y$. Please note that this is not the same as distance. Only the larger difference in coordinate is available.

For example, Given the straight line with coordinates $(0,0)$ and $(9,4)$ with the larger 'delta' as '3', we need to find the point $(x_2,y_2)$ with this delta.



Note that the slope of the line is $$ m=\frac{y_3-y_1}{x_3-x_1} $$

and, for a point $P=(x_2,y_2)=(x_1+\Delta x,y_1+\Delta y)$ on this line we have: $$ m>1 \quad \rightarrow \quad \Delta x >\Delta y $$ $$ m<1 \quad \rightarrow \quad \Delta y >\Delta x $$

and for $m=1$ the two delta are the same. Can you see why? And can you do from this?

  • $\begingroup$ Thank you! So, using this, I can find out whether the delta that I have is with respect to x or y . Can you please help me understand how to find the other coordinate ? $\endgroup$ – Manjunath Reddy Aug 17 '16 at 10:14
  • $\begingroup$ Use the equation of the line: $y-y_1=m(x-x_1)$ substituting $x=x_1+\Delta x$ or $y=y_1+\Delta y$. $\endgroup$ – Emilio Novati Aug 17 '16 at 10:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.