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Question Number 105273 by ajfour last updated on 27/Jul/20

Commented by ajfour last updated on 27/Jul/20

Given P(h,k) and B(p,q) To find image I(r,t) of B(p,q) in the mirror line AT.

GivenP(h,k)andB(p,q)TofindimageI(r,t)ofB(p,q)inthemirrorlineAT.

Answered by mr W last updated on 28/Jul/20

T(m,m^2 ) tan θ=((b−m^2 )/(a−m))=2m m^2 −2am+b=0 ⇒m=a+(√(a^2 −b)) eqn. of AP: y=b+2m(x−a) ⇒2mx−y+b−2ma image of B(p,q) is (r,t): r=p−((4m(2mp−q+b−2ma))/(4m^2 +1)) t=q+((2(2mp−q+b−2ma))/(4m^2 +1)) image of P(h,k) is (f,g): f=h−((4m(2mh−k+b−2ma))/(4m^2 +1)) g=k+((2(2mh−k+b−2ma))/(4m^2 +1))

T(m,m2)tanθ=b−m2a−m=2mm2−2am+b=0⇒m=a+a2−beqn.ofAP:y=b+2m(x−a)⇒2mx−y+b−2maimageofB(p,q)is(r,t):r=p−4m(2mp−q+b−2ma)4m2+1t=q+2(2mp−q+b−2ma)4m2+1imageofP(h,k)is(f,g):f=h−4m(2mh−k+b−2ma)4m2+1g=k+2(2mh−k+b−2ma)4m2+1

Commented by mr W last updated on 28/Jul/20

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