问题
填空题
已知直线l1过点A(-2,3),B(4,m),直线l2过点M(1,0),N(0,m-4),若l1⊥l2,则常数m的值是______.
答案
∵直线l1过点A(-2,3),B(4,m),
∴直线l1的斜率k1=
=m-3 4-(-2)
,m-3 6
同理直线l2过点M(1,0),N(0,m-4),
故直线l2的斜率k2=
,m-4 -1
因为l1⊥l2,所以k1•k2=
•m-3 6
=-1,m-4 -1
即m2-7m+6=0,分解因式可得(m-1)(m-6)=0,
解得m=1或m=6,
故答案为:1或6