Answer:
(D)Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals
Step-by-step explanation:
Let us verify the choosen option
In Quadrilateral ABCD with points A(-2,0), B(0,-2), C(-3,-5), D(-5,-3)
Using the distance formula
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]|AB|=\sqrt{(0-(-2))^2+(-2-0)^2}=\sqrt{8}=2\sqrt{2}\\|CD|=\sqrt{(-5+3))^2+(-3+5)^2}=\sqrt{8}=2\sqrt{2}\\|BC|=\sqrt{(-3-0))^2+(-5+2)^2}=\sqrt{18}=3\sqrt{2}\\|AD|=\sqrt{(-5+2)^2+(-3-0)^2}=\sqrt{18}=3\sqrt{2}\\[/tex]
Since |AB| is congruent to |CD| and |BC| is congruent to |AD|, we conclude that opposite sides are congruent.
Next, let us consider the slope.
Slope of |AB|= [tex]\frac{-2-0}{0-(-2)} =\frac{-2}{2}=-1[/tex]
Slope of |BC|[tex]=\frac{-5+2}{-3-0} =\frac{-3}{-3}=1[/tex]
Since the slopes of consecutive sides are opposite reciprocals, therefore ABCD is a rectangle.
Option D is the correct option.
Answer:
the answers will be D
Step-by-step explanation:
prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals
