两点式方程化简

问题描述

精选答案

(y-y1)/(x-x1)=(y2-y1)/(x2-x1) ，令(y2-y1)/(x2-x1)=A；

(y-y3)/(x-x3)=(y4-y3)/(x4-x3) ，令(y4-y3)/(x4-x3)=B；

y-y1 = Ax-Ax1 -------------------------------(1)

y-y3 = Bx-Bx3-------------------------------(2)

(1)-(2).

y3-y1=(A-B)x-Ax1+Bx3

x=[y3-y1+Ax1-Bx3]/(A-B)----------------------(3)

从(1), By-By1=ABx-ABx1----------------------(4)

从(2), Ay-Ay3=ABx-ABx3-----------------------(5)

(4)-(5)

y(B-A)-By1+Ay3=ABx3-ABx1

y={AB(x3-x1)+By1-Ay3}/(B-A)---------------(6)

答案见: (3),(6)