The endpoints of one diagonal of a rhombus are (-5,2) and (1,6). If the coordinates of the 3rd vertexare (-6,10), what arethe coordinates of the 4th vertex?
A.(2,-2)
B.(-8,0)
C.(4,8)
D.(-9,8)

Look at the picture.

[tex]E\left(\dfrac{-5+1}{2};\ \dfrac{2+6}{2}\right)\to E\left(\dfrac{-4}{2};\ \dfrac{8}{2}\right)\to E(-2;\ 4)[/tex]

[tex]\vec{BE}=[-2-(-6);\ 4-10]=[4;\ -6][/tex]

[tex]D(x;\ y)\\\\\vec{ED}=[x-(-2);\ y-4]=[x+2;\ y-4]\\\\\vec{ED}=\vec{BE}\ therefore\\\\ \ [x+2;\ y-4]=[4;\ -6]\to x+2=4\ and\ y-4=-6\\\\x=2\ and\ y=-2\\\\Answer:\ \boxed{A.\ (2;\ -2)}[/tex]

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The endpoints of one diagonal of a rhombus are (-5,2) and (1,6). If the coordinates of the 3rd vertexare (-6,10), what arethe coordinates of the 4th vertex? A.(2,-2) B.(-8,0) C.(4,8) D.(-9,8)

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The endpoints of one diagonal of a rhombus are (-5,2) and (1,6). If the coordinates of the 3rd vertexare (-6,10), what arethe coordinates of the 4th vertex?
A.(2,-2)
B.(-8,0)
C.(4,8)
D.(-9,8)