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3 years ago

Answer will mark Brainliest

Mathematics

1 answer:

lidiya [134]3 years ago

5 0

H’(-2,0) and J’’ 0,6

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The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

daser333 [38]

Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}$

$EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}$

$FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}$

$DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}$

Slope formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of DE,

$m_1=\frac{4-5}{2+2}= \frac{-1}{4}$

Slope of EF,

$m_2=\frac{0-4}{0-2}= 2$

Slope of FG,

$m_3=\frac{1-0}{-4-0}= \frac{-1}{4}$

Slope of DG,

$m_4=\frac{1-5}{-4+2}= 2$

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

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