A) \[y=7\]
B) \[6x+y-19=0\]
C) \[x+2y-7=0\]
D) \[6x+2y-19=0\]
Correct Answer: B
Solution :
Slope of the line segment joining (-4,6) and (8,8) is given by \[\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\frac{8-6}{8+4}=\frac{2}{12}=\frac{1}{6}\] \[\therefore \] Slope of line perpendicular to it is \[m=-\frac{1}{\frac{1}{6}}=-6\] As the line bisecting it. \[\therefore \] Mid point of this Line is \[\left( \frac{8-4}{2},\frac{8+6}{2} \right)=\,(2,7)\] \[\therefore \] The equation of the line segment bisecting perpendicularly the given line is given by \[y-{{y}_{1}}=m\,(x-{{x}_{1}})\] and here we have \[({{x}_{1}},\,{{y}_{1}})=(2,7)\] \[m=-6\] \[\therefore \] Required equation is \[y-7=-6\,(x-2)\] \[y-7=-6x+12\] \[y+6x-19=0\] or \[6x+y-19=0\]
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