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The Maxima on-line user's manual

Algebra Calculator

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Fourth

Function: fourth (<expr>) Returns the 4th item of expression or list <expr>. See first for more details.

a : 0;
 b : 1;
sol : first(solve ([a*x_p + b*y_p + c = 0, a*x_q + b*y_q + c = 0, a*x_r + b*y_r + c = 0, x_1*y_p + (0 - x_p)*y_1 = t_1*y_p, x_1*y_q + (t_2 - x_q)*y_1 = t_2*y_q, x_1*y_r + (t_3 - x_r)*y_1 = t_3*y_r],[x_p,y_p,x_q,y_q,x_r,y_r]));
sol2 : solve(at ([x_2*y_p + (t_1pr - x_p)*y_2 = t_1pr*y_p,x_2*y_q + (t_2pr - x_q)*y_2 = t_2pr*y_q,x_2*y_r + (t_3pr - x_r)*y_2 = t_3pr*y_r], sol),[x_1,y_1,x_2,y_2,c]), ratsimp;
tex(fourth(sol2));

(%o1)                                true
(%i2) 

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