A(1,5)B(4,1)C(2,-1) mx-y-2m+6=0与△ABC恒有公共点,实数m的取值范围是

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A(1,5)B(4,1)C(2,-1) mx-y-2m+6=0与△ABC恒有公共点,实数m的取值范围是
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A(1,5)B(4,1)C(2,-1) mx-y-2m+6=0与△ABC恒有公共点,实数m的取值范围是
A(1,5)B(4,1)C(2,-1) mx-y-2m+6=0与△ABC恒有公共点,实数m的取值范围是

A(1,5)B(4,1)C(2,-1) mx-y-2m+6=0与△ABC恒有公共点,实数m的取值范围是
依题设,得 直线mx-y-2m+6=(x-2)m+(6-y)=0过定点M(2,6),斜率为m,且MC⊥x轴,则
m≥kMA=1或m≤kMB=-5/2

mx-y-2m+6=0即y=mx-2m+6过定点M(2,6)斜率是m
画图易知m∈﹙﹣∞,kMB]∪[kMA,﹢∞﹚
即m∈﹙﹣∞,﹣2.5]∪[1,﹢∞﹚