Say one has two points in the x,y plane. How would one convert those two points lớn a line? Of course I know you could use the slope-point formula và derive the line as following:\$\$y - y_0 = fracy_1-y_0x_1-x_0(x-x_0)\$\$However this manner obviously doesn"t hold when \$x_1-x_0 = 0\$ (vertical line). The more generic approach should however be capable of define every line (vertical line would simply mean B = 0);\$\$Ax+By +C = 0\$\$

But how to lớn deduce A, B, C given two points?

Let \$P_1:(x_1,y_1)\$ & \$P_2:(x_2,y_2)\$. Then a point \$P:(x,y)\$ lies on the line connecting \$P_1\$ và \$P_2\$ if và only if the area of the parallellogram with sides \$P_1P_2\$ and \$P_1P\$ is zero. This can be expressed using the determinant as\$\$eginvmatrixx_2-x_1 & x-x_1 \y_2-y_1 & y-y_1endvmatrix = 0 Longleftrightarrow(y_1-y_2)x+(x_2-x_1)y+x_1y_2-x_2y_1=0,\$\$so you get (up lớn scale) \$A=y_1-y_2\$, \$B=x_2-x_1\$ & \$C=x_1y_2-x_2y_1\$.

Bạn đang xem: Converting y=mx+b into ax+by+c=0 and vice versa

Thanks for contributing an answer lớn magmareport.netematics Stack Exchange!

Please be sure to answer the question. Provide details & share your research!

But avoid

Asking for help, clarification, or responding to lớn other answers.Making statements based on opinion; back them up with references or personal experience.

Use magmareport.netJax khổng lồ format equations. magmareport.netJax reference.

Xem thêm: Tải Bộ Đề Thi Giữa Kì Tiếng Anh Lớp 7 Giữa Học Kì 1 Có Đáp Án Năm 2021

To learn more, see our tips on writing great answers.

Post Your Answer Discard

By clicking “Post Your Answer”, you agree khổng lồ our terms of service, privacy policy và cookie policy

## Not the answer you're looking for? Browse other questions tagged algebra-precalculus analytic-geometry or ask your own question.

Line determined by two points is \$fracx - x_0x_1 - x_0 = fracy - y_0y_1 - y_0 = fracz - z_0z_1 - z_0\$
Prove that for any circle in R^2, if two ordered pairs on the circle are separated by 180 degrees, then the connecting line passes through the center

Site design / biểu tượng logo © 2022 Stack Exchange Inc; user contributions licensed under cc by-sa. Rev2022.6.24.42450

Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device và disclose information in accordance with our Cookie Policy.