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Question Number 8243 by lepan last updated on 04/Oct/16

$$Findtheequationoftheperpendicularbisectorofthelinejoiningthepoints(-5,4)tothepoint(9,-3)$$$$$$

Answered by sandy_suhendra last updated on 04/Oct/16

$$\mathrm{let}\mathrm{A}(-5,4)\mathrm{and}\mathrm{B}(9,-3)$$$$\mathrm{P}\mathrm{is}\mathrm{midpoint}\mathrm{of}\mathrm{AB}\mathrm{so}\mathrm{P}(\frac{-5+9}{2},\frac{4-3}{2})=\mathrm{P}(2,\frac{1}{2})$$$$\mathrm{the}\mathrm{gradient}\mathrm{of}\mathrm{AB}={\mathrm{m}}_{\mathrm{AB}}=\frac{{\mathrm{y}}_{\mathrm{A}}-{\mathrm{y}}_{\mathrm{B}}}{{\mathrm{x}}_{\mathrm{A}}-{\mathrm{x}}_{\mathrm{B}}}=\frac{4+3}{-5-9}=-\frac{1}{2}$$$$\mathrm{the}\mathrm{gradient}\mathrm{of}\mathrm{the}\mathrm{perpendicular}\mathrm{bisector}={\mathrm{m}}_1$$$$\mathrm{so}{\mathrm{m}}_{\mathrm{AB}}\times {\mathrm{m}}_1=-1$$$$-\frac{1}{2}\times {\mathrm{m}}_1=-1$$$${\mathrm{m}}_1=2$$$$\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{perpendicular}\mathrm{bisector}:$$$$\mathrm{y}-{\mathrm{y}}_{\mathrm{P}}={\mathrm{m}}_1(\mathrm{x}-{\mathrm{x}}_{\mathrm{P}})$$$$\mathrm{y}-2=2(\mathrm{x}-\frac{1}{2})$$$$\mathbf{y}=2\mathbf{x}+1$$

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