Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 78820 by mathocean1 last updated on 20/Jan/20

please what is the fomula to determinate the equations of bissectors in triangle?

$$\mathrm{please}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{fomula}\:\mathrm{to}\: \\ $$$$\mathrm{determinate}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\: \\ $$$$\mathrm{bissectors}\:\mathrm{in}\:\mathrm{triangle}? \\ $$

Answered by MJS last updated on 21/Jan/20

bisector between 2 lines l_1 : y=a_1 x+c_1 l_2 : y=a_2 x+c_2 intersection: I= ((((c_2 −c_1 )/(a_1 −a_2 ))),(((a_1 c_2 −a_2 c_1 )/(a_1 −a_2 ))) ) direction vectors: v_1 = ((1),(a_1 ) ); v_2 = ((1),(a_2 ) ) normalized: v_1 = (((1/(√(1+a_1 ^2 )))),((a_1 /(√(1+a_1 ^2 )))) ) ; v_2 = (((1/(√(1+a_2 ^2 )))),((a_1 /(√(1+a_2 ^2 )))) ) direction vectors of bisectors v_(b1) =v_1 +v_2 = ((p),(q) ) v_(b2) = ((q),((−p)) ) bisectors l_(b1) : X=I+tv_(b1) l_(b2) : X=I+tv_(b2)

$$\mathrm{bisector}\:\mathrm{between}\:\mathrm{2}\:\mathrm{lines} \\ $$$${l}_{\mathrm{1}} :\:{y}={a}_{\mathrm{1}} {x}+{c}_{\mathrm{1}} \\ $$$${l}_{\mathrm{2}} :\:{y}={a}_{\mathrm{2}} {x}+{c}_{\mathrm{2}} \\ $$$$\mathrm{intersection}: \\ $$$${I}=\begin{pmatrix}{\frac{{c}_{\mathrm{2}} −{c}_{\mathrm{1}} }{{a}_{\mathrm{1}} −{a}_{\mathrm{2}} }}\\{\frac{{a}_{\mathrm{1}} {c}_{\mathrm{2}} −{a}_{\mathrm{2}} {c}_{\mathrm{1}} }{{a}_{\mathrm{1}} −{a}_{\mathrm{2}} }}\end{pmatrix} \\ $$$$\mathrm{direction}\:\mathrm{vectors}: \\ $$$${v}_{\mathrm{1}} =\begin{pmatrix}{\mathrm{1}}\\{{a}_{\mathrm{1}} }\end{pmatrix};\:{v}_{\mathrm{2}} =\begin{pmatrix}{\mathrm{1}}\\{{a}_{\mathrm{2}} }\end{pmatrix} \\ $$$$\mathrm{normalized}: \\ $$$${v}_{\mathrm{1}} =\begin{pmatrix}{\frac{\mathrm{1}}{\sqrt{\mathrm{1}+{a}_{\mathrm{1}} ^{\mathrm{2}} }}}\\{\frac{{a}_{\mathrm{1}} }{\sqrt{\mathrm{1}+{a}_{\mathrm{1}} ^{\mathrm{2}} }}}\end{pmatrix}\:;\:{v}_{\mathrm{2}} =\begin{pmatrix}{\frac{\mathrm{1}}{\sqrt{\mathrm{1}+{a}_{\mathrm{2}} ^{\mathrm{2}} }}}\\{\frac{{a}_{\mathrm{1}} }{\sqrt{\mathrm{1}+{a}_{\mathrm{2}} ^{\mathrm{2}} }}}\end{pmatrix} \\ $$$$\mathrm{direction}\:\mathrm{vectors}\:\mathrm{of}\:\mathrm{bisectors} \\ $$$${v}_{{b}\mathrm{1}} ={v}_{\mathrm{1}} +{v}_{\mathrm{2}} =\begin{pmatrix}{{p}}\\{{q}}\end{pmatrix} \\ $$$${v}_{{b}\mathrm{2}} =\begin{pmatrix}{{q}}\\{−{p}}\end{pmatrix} \\ $$$$\mathrm{bisectors} \\ $$$${l}_{{b}\mathrm{1}} :\:{X}={I}+{tv}_{{b}\mathrm{1}} \\ $$$${l}_{{b}\mathrm{2}} :\:{X}={I}+{tv}_{{b}\mathrm{2}} \\ $$

Commented by jagoll last updated on 21/Jan/20

good sir

$$\mathrm{good}\:\mathrm{sir} \\ $$

Commented by mathocean1 last updated on 21/Jan/20

hello is it the same thing of bissectrice of angles?

$$\mathrm{hello} \\ $$$$\mathrm{is}\:\mathrm{it}\:\mathrm{the}\:\mathrm{same}\:\mathrm{thing}\:\mathrm{of}\: \\ $$$$\mathrm{bissectrice}\:\mathrm{of}\:\mathrm{angles}? \\ $$

Commented by MJS last updated on 21/Jan/20

of course. what is an angle without lines?

$$\mathrm{of}\:\mathrm{course}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{without}\:\mathrm{lines}? \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com