1
$\begingroup$

I would like to find a point $d$ away on a line from a starting point only given a slope. My fist thought was to use the distance formula ($d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$), but I would have to solve for two variables. How can I solve find the point without graphing or brute forcing?

$\endgroup$
2
$\begingroup$

If $m$ is the given slope, you also have $y_2-y_1=m(x_2-x_1)$, so $$d=\sqrt{1+m^2}|x_2-x_1|\\x_2=x_1\pm \frac d{\sqrt{1+m^2}}$$

$\endgroup$

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.