Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

The coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).



To determine if it is a parallelogram, use the converse of the parallelogram diagonal theorem. This states that if the diagonals
, then the quadrilateral is a parallelogram.



The midpoint of HJ is
and the midpoint of IK is (2, 2).



Therefore, HIJK is a parallelogram because the diagonals
, which means they bisect each other.

Sagot :

Check the picture below.

well, HIJK is a parallelogram only if its diagonals bisect each other, if that's so, the midpoint of HJ is the same as the midpoint of IK, let's check

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad J(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 + 0}{2}~~~ ,~~~ \cfrac{ -1 + 5}{2} \right)\implies \left( \cfrac{4}{2}~~,~~\cfrac{4}{2} \right)\implies \boxed{(2~~,~~2)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ I(\stackrel{x_1}{3}~,~\stackrel{y_1}{3})\qquad K(\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \left(\cfrac{ 1 + 3}{2}~~~ ,~~~ \cfrac{ 1 + 3}{2} \right)\implies \boxed{(2~~,~~2)}[/tex]

View image jdoe0001
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.