What kind of shape has vertices #A(-1, -4), B(1, -1), C(4,1), D(2, -2)#?

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Answer 1 · 2018-06-10T14:45:18

Shape of the figure is a SQUARE

#A(-1,-4), B(1,-1), C(4,1), D(2,-2)#

Slope of #bar(AB) = (-1+4) / (1 + 1) = 3/2#

Slope of #bar (CD) = (-2-1) / (2-4) = 3/2#

Slope of #bar(BC) = (1+1)/(4-3) = -2/3#

Slope of #bar (AD) = (-2+4) / (2+1) = -2/3#

# vec(AB)# “parallel “ #vec(CD), vec(BC)# “ parallel “ #vec(AD)#

#vec(AB) # “ perpendicular “ #vec(BC)#, #vec(CD)# “ perpendicular “ vec(AD)#

#vec(AB) = sqrt((1+1)^2 + (-1+4)^2) = sqrt13#

#vec(BC) = sqrt((4-1)^2 + (1+1)^2) = sqrt13#

Hence #vec(AB) = vec(BC)#

Therefore the shape of the figure is a SQUARE