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Question Number 121393 by faysal last updated on 07/Nov/20
a square′s one diagonal′s terminal points are  (5,0), (9,4) what are the coordinate of  other diagonal′s terminal points
asquaresonediagonalsterminalpointsare(5,0),(9,4)whatarethecoordinateofotherdiagonalsterminalpoints
Answered by TANMAY PANACEA last updated on 07/Nov/20
Disgonal eqn  ((y−0)/(0−4))=((x−5)/(5−9))→x−y−5=0  mid point of(5,0) and(9,4)=(7,2)  another diagonal is ⊥(x−y−5=0)is  x+y=k which passes through (7,2)→7+2=k  Eqn anothdr diagonal  x+y=9  the side of square make 45^o  with diagonal  x−y=5 snd which passes through (5,0)is  y=m(x−5) →slope of x−y=5 is 1  tan45^0 =((1−m)/(1+m))→m=0   eqn of side is y=0  (x axis)  solve y=0  and x+y=9  (9,0)is one terminal of another diagonal  the side of square make 45^o  with diagonal x−y=5  and passes through(9,4) is (y−4)=m_1 (x−9)  tan45^o =((1−m_1 )/(1+m_1 ))→m_1 =0  eqn of anothdr side y=4  solve y=4  and x+y=9    another terminal(5,4)  Rewuired answer is (9,0) and (5,4)
Disgonaleqny004=x559xy5=0midpointof(5,0)and(9,4)=(7,2)anotherdiagonalis(xy5=0)isx+y=kwhichpassesthrough(7,2)7+2=kEqnanothdrdiagonalx+y=9thesideofsquaremake45owithdiagonalxy=5sndwhichpassesthrough(5,0)isy=m(x5)slopeofxy=5is1tan450=1m1+mm=0eqnofsideisy=0(xaxis)solvey=0andx+y=9(9,0)isoneterminalofanotherdiagonalthesideofsquaremake45owithdiagonalxy=5andpassesthrough(9,4)is(y4)=m1(x9)tan45o=1m11+m1m1=0eqnofanothdrsidey=4solvey=4andx+y=9anotherterminal(5,4)Rewuiredansweris(9,0)and(5,4)
Answered by mr W last updated on 07/Nov/20
((5+9)/2)=7  ((0+4)/2)=2  ((4−0)/(9−5))=1  (√((9−5)^2 +(4−0)^2 ))=4(√2)  (7,2)±((4(√2))/2)((1/( (√2))),−(1/( (√2))))=(7±2,2∓2)  =(9,0) and (5,4)
5+92=70+42=24095=1(95)2+(40)2=42(7,2)±422(12,12)=(7±2,22)=(9,0)and(5,4)

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