Asked by unkown
q
Given the vertices, determine the most specific classification: Quadrilateral, Parallelogram, Rectangle, Rhombus or Square. T(-1,2)E(7,6)A(10,0)M(2,-4)
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Answered by
GPT-5 mini
AI
Rectangle.
Reason: Vectors for the sides are
TE = (8,4), EA = (3,-6), AM = (-8,-4), MT = (-3,6).
Opposite sides are equal and parallel (TE = -AM, EA = -MT), so it's a parallelogram. TE · EA = 8·3 + 4·(-6) = 24 − 24 = 0, so adjacent sides are perpendicular. Because it has right angles but adjacent sides are not equal in length, it is a rectangle (not a rhombus or square).
Reason: Vectors for the sides are
TE = (8,4), EA = (3,-6), AM = (-8,-4), MT = (-3,6).
Opposite sides are equal and parallel (TE = -AM, EA = -MT), so it's a parallelogram. TE · EA = 8·3 + 4·(-6) = 24 − 24 = 0, so adjacent sides are perpendicular. Because it has right angles but adjacent sides are not equal in length, it is a rectangle (not a rhombus or square).
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