3 years ago

PLS HELP! The picture is down below

Mathematics

1 answer:

Alex_Xolod [135]3 years ago

4 0

Answer: D
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Parallelogram ABCD has vertices at A(2,-3), B(8,-6), Cl14,-3), and D(8,0)

OlgaM077 [116]

Answer:

The correct option is C.

Step-by-step explanation:

The vertices of ABCD are A(2,-3), B(8,-6), C(14,-3), and D(8,0).

Distance formula:

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

The length of sides are

$AB=\sqrt{(8-2)^2+(-6+3)^2}=\sqrt{36+9}=\sqrt{45}$

$BC=\sqrt{(14-8)^2+(-3+6)^2}=\sqrt{36+9}=\sqrt{45}$

$CD=\sqrt{(8-14)^2+(0-3)^2}=\sqrt{36+9}=\sqrt{45}$

$AD=\sqrt{(8-2)^2+(0+3)^2}=\sqrt{36+9}=\sqrt{45}$

Since length of all sides are equation therefore the given parallelogram cannot be a rectangle.

Slope formula:

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

Slope of AB is

$m_1=\frac{-6-(-3)}{8-2}=\frac{-3}{6}=\frac{-1}{2}$

Slope of BC is

$m_2=\frac{-3-(-6)}{14-8}=\frac{3}{6}=\frac{1}{2}$

Since the slopes of two consecutive sides are not opposite reciprocals, therefore the given parallelogram is a rhombus. Option C is correct.

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