Respuesta :
Length of diagonals are :
[tex]D_1 = \sqrt{ (-5-(-1))^2 + (1-(-2))^2 }\\\\D_1 = 5\ units[/tex]
[tex]D_2 = \sqrt{(-2 -2 )^2 + (5-2)^2}\\\\D_2 = 5 \ units[/tex]
Now, Slope of both the diagonal is :
[tex]m_1 =\dfrac{1-(-2)}{-5-(-1)} \\\\m_1 = -\dfrac{3}{4}\\\\m_2 = \dfrac{5-2}{-2-2}\\\\m_2 = -\dfrac{3}{4}[/tex]
Now, product of slopes are :
[tex]m_1 \times m_2 = \dfrac{-3}{4} \times \dfrac{-3}{4}\\\\m_1 \times m_2 = \dfrac{9}{16}[/tex]
Since, the product of slope is not equal to -1 . It means that the slopes are not perpendicular.
Therefore, this quadrilateral is not square.
