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

Answer 1

Violet Aldrich

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

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Answer 2

Evelyn Arboleda

The shape formed by the given vertices A(-1, -4), B(1, -1), C(4,1), D(2, -2) is a quadrilateral. Specifically, it is a quadrilateral with the vertices arranged in the order ABCD, forming a convex shape. Without additional information about the lengths of the sides or the measures of the angles, it is not possible to determine the specific type of quadrilateral (e.g., parallelogram, trapezoid, kite, etc.).

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