The points A(-4, -1),B(-2, -4),C(4, 0),and D( | vedclass

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(B) Let the vertices be $A(-4, -1)$,$B(-2, -4)$,$C(4, 0)$,and $D(2, 3)$.First,we check the mid-points of the diagonals $AC$ and $BD$:Mid-point of $AC

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Rectangle

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(B) Let the vertices be $A(-4, -1)$,$B(-2, -4)$,$C(4, 0)$,and $D(2, 3)$.First,we check the mid-points of the diagonals $AC$ and $BD$:Mid-point of $AC = (\frac{-4+4}{2}, \frac{-1+0}{2}) = (0, -0.5)$.Mid-point of $BD = (\frac{-2+2}{2}, \frac{-4+3}{2}) = (0, -0.5)$.Since the mid-points are the same,the figure is a parallelogram.Next,we calculate the slopes of adjacent sides $AB$ and $AD$:Slope of $AB$ $(m_1)$ = $\frac{-4 - (-1)}{-2 - (-4)} = \frac{-3}{2}$.Slope of $AD$ $(m_2)$ = $\frac{3 - (-1)}{2 - (-4)} = \frac{4}{6} = \frac{2}{3}$.Since $m_1 	imes m_2 = (\frac{-3}{2}) 	imes (\frac{2}{3}) = -1$,the adjacent sides are perpendicular.Therefore,the figure is a rectangle.

The points $A(-4, -1)$,$B(-2, -4)$,$C(4, 0)$,and $D(2, 3)$ are the vertices of:

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