Answer:
DOGS is a parallelogram.
Step-by-step explanation:
Given the quadrilateral DOGS with coordinates D(1, 1), O(2, 4), G(5, 6), and S(4,3).
To prove that it is a parallelogram, we need to show that the opposite lengths are equal. That is:
Using the Distance Formula
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For D(1, 1) and O(2, 4)
[tex]|DO|=\sqrt{(2-1)^2+(4-1)^2}=\sqrt{1^2+3^2}=\sqrt{10} \:Units[/tex]
For G(5, 6), and S(4,3).
[tex]|GS|=\sqrt{(4-5)^2+(3-6)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{10}\:Units[/tex]
For O(2, 4) and G(5, 6)
[tex]|OG|=\sqrt{(5-2)^2+(6-4)^2}=\sqrt{(3)^2+(2)^2}=\sqrt{13}\:Units[/tex]
For S(4,3) and D(1, 1)
[tex]|SD|=\sqrt{(1-4)^2+(1-3)^2}=\sqrt{(-3)^2+(-2)^2}=\sqrt{13}\:Units[/tex]
Since:
Then, quadrilateral DOGS is a parallelogram.
