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ABCD-is-a-square-AC-is-a-diagonal-If-the-coordinate-of-A-C-are-5-8-and-7-4-Find-the-coordinate-of-B-and-D-




Question Number 58984 by Tawa1 last updated on 02/May/19
ABCD  is a square, AC is a diagonal. If  the coordinate of  A, C  are  (− 5, 8) and (7, − 4) . Find the coordinate of  B and D.
ABCDisasquare,ACisadiagonal.IfthecoordinateofA,Care(5,8)and(7,4).FindthecoordinateofBandD.
Answered by tanmay last updated on 02/May/19
AC eqn (y−8)=((8+4)/(−5−7))(x+5)  y−8=−x−5  x+y=3→ y=−x+3  slope m=(−1)  the eqn of st line passing through(−5,8)   y−8=m_1 (x+5)  the angle between x+y=3 and (y−8)=m_1 (x+5)  is 45^0   tan45^o =((m_1 −(−1))/(1+m_1 (−1)))    m_1 +1=1−m_1   m_1 =0  so eqn is (y−8)=0×(x+5)  y=8←eqn of AD  the eqn ∥ to y=8 passing through (7,−4) is  y=−4 →eqn of BC  so eqn of AB  x=−5 (  eqn of CD is x=7  so AB→x+5=0   CD  is x−7=0  BC is y+4=0  DA is y−8=0    A(−5,8)  B(−5,−4)   C(7,−4)  D(7,8)
ACeqn(y8)=8+457(x+5)y8=x5x+y=3y=x+3slopem=(1)theeqnofstlinepassingthrough(5,8)y8=m1(x+5)theanglebetweenx+y=3and(y8)=m1(x+5)is450tan45o=m1(1)1+m1(1)m1+1=1m1m1=0soeqnis(y8)=0×(x+5)y=8eqnofADtheeqntoy=8passingthrough(7,4)isy=4eqnofBCsoeqnofABx=5(eqnofCDisx=7soABx+5=0CDisx7=0BCisy+4=0DAisy8=0A(5,8)B(5,4)C(7,4)D(7,8)
Commented by Tawa1 last updated on 02/May/19
God bless you sir
GodblessyousirGodblessyousir
Commented by tanmay last updated on 02/May/19
thank you...
thankyouthankyou

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