Question

Show that the points (1, 7), 14, 2, (-1, -1) and (-4, 4) are the vertices of a
square.​

Answer 1

First of all the question is worng .The coordinates should be (1,7),(4,2),(-1,-1),(-4,4)

Now taking the cordinates give above

let, a=(1,7), b=(4,2), c=(-1,-1), d(-4,4)

if the given co ordinates form a square then the length between each co ordinate must be equal

therefore to prove,  ab=bc=cd=ad

ab=√(1-4)^2+(7-2)^2

   = 6

bc=√(4+1)^2+(2+1)^2

   = 6

cd=√(4-1)^2+(4+1)^2

   = 6

ad=√(4+1)^2+(7-4)^2

   = 6

∴ ab=bc=cd=ad

           ∴ a,b,c,d co-ordinates fom a square

                                       HENCE PROVED