Question 155793
First lets find the length of PQ




{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}} Start with the distance formula.



{{{d=sqrt((4-1)^2+(-4--6)^2)}}} Plug in {{{x[1]=4}}},  {{{x[2]=1}}}, {{{y[1]=-4}}}, and {{{y[2]=-6}}}.



{{{d=sqrt((3)^2+(-4--6)^2)}}} Subtract {{{1}}} from {{{4}}} to get {{{3}}}.



{{{d=sqrt((3)^2+(2)^2)}}} Subtract {{{-6}}} from {{{-4}}} to get {{{2}}}.



{{{d=sqrt(9+(2)^2)}}} Square {{{3}}} to get {{{9}}}.



{{{d=sqrt(9+4)}}} Square {{{2}}} to get {{{4}}}.



{{{d=sqrt(13)}}} Add {{{9}}} to {{{4}}} to get {{{13}}}.



So the length of PQ is {{{sqrt(13)}}} units



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Now let's find the length of QR




{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}} Start with the distance formula.



{{{d=sqrt((1--1)^2+(-6--3)^2)}}} Plug in {{{x[1]=1}}},  {{{x[2]=-1}}}, {{{y[1]=-6}}}, and {{{y[2]=-3}}}.



{{{d=sqrt((2)^2+(-6--3)^2)}}} Subtract {{{-1}}} from {{{1}}} to get {{{2}}}.



{{{d=sqrt((2)^2+(-3)^2)}}} Subtract {{{-3}}} from {{{-6}}} to get {{{-3}}}.



{{{d=sqrt(4+(-3)^2)}}} Square {{{2}}} to get {{{4}}}.



{{{d=sqrt(4+9)}}} Square {{{-3}}} to get {{{9}}}.



{{{d=sqrt(13)}}} Add {{{4}}} to {{{9}}} to get {{{13}}}.



So the length of QR is {{{d=sqrt(13)}}} 



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Answer:


Since {{{PQ=sqrt(13)}}} and {{{QR=sqrt(13)}}}, this means that {{{PQ=QR}}}