The coordinates of the vertices of quadrilateral rstu are r(−4, 1) , s(4, −1) , t(3, −6) , and u(−5, −4) . which statement correctly describes whether quadrilateral rstu is a rectangle?

For k12- the answer is Quadrilateral RSTU is not a rectangle because it has no right angles.

Step-by-step explanation:

Solution: A quadrilateral RSTU whose vertices are  R(−4, 1) , S(4, −1) , T(3, −6) , and U(−5, −4).

RS =

ST=

TU=

UR =

→RS=TU, and ST=UR⇒ Opposite sides are equal.

Slope of RS =

Slope of TS=

Slope of RS × Slope of TS = -1/4 × 5 = -5/4 ≠ -1, So lines are not perpendicular.

∴ quadrilateral RSTU  is not a rectangle.

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