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\$.

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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