Mathematics: 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?

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The coordinates of the vertices of quadrilateral

AT3P

31.05.2020

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

Step-by-step explanation:

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leannadoughty06

13.03.2022

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

RS = $\sqrt{(4+4)^{2}+(-1-1)^{2}} =\sqrt{64+4}= \sqrt{68}$

ST= $\sqrt{(4-3)^{2}+(-1+6)^{2}}= \sqrt{1+25} =\sqrt{26}$

TU= $\sqrt{(3+5)^{2}+(-6+4)^{2}}= \sqrt{64+4}= \sqrt{68}$

UR = $\sqrt{(-5+4)^{2}+(-4-1)^{2}}= \sqrt{1+25} =\sqrt{26}$

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

Slope of RS = $\frac{-1-1}{4+4} = \frac{-2}{8}= \frac{-1}{4}$

Slope of TS= $\frac{-6+1}{3-4} =\frac{-5}{-1}=5$

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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