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Question Number 46816 by peter frank last updated on 31/Oct/18

Answered by tanmay.chaudhury50@gmail.com last updated on 01/Nov/18

slope M_1 =(((a/m_(2 ) )−(a/m_1 ))/(a(m_2 −m_1 ))) M_1 =((a(m_1 −m_2 ))/(am_1 m_2 (m_2 −m_1 )))=((−1)/(m_1 m_2 )) slope M_2 =(((a/m_4 )−(a/m_3 ))/(a(m_4 −m_3 )))=((−1)/(m_3 m_4 )) M_1 ×M_2 =−1 (since line 1⊥ to second line) M_1 ×M_2 =((−1)/(m_1 m_2 ))×((−1)/(m_3 m_4 ))=−1 hence m_1 m_2 m_3 m_4 =−1 proved

slopeM1=am2−am1a(m2−m1)M1=a(m1−m2)am1m2(m2−m1)=−1m1m2slopeM2=am4−am3a(m4−m3)=−1m3m4M1×M2=−1(sinceline1⊥tosecondline)M1×M2=−1m1m2×−1m3m4=−1hencem1m2m3m4=−1proved

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