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marin [14]
2 years ago
8

The end points of one diagonal of a rhombus are (-5,2) and (1,6). If the coordinates of the 3rd vertexare (-6,10), what are the

coordinates of the 4th vertex?
A.(2,-2)
B.(-8,0)
C.(4,8)
D(-9,8)

Mathematics
1 answer:
ad-work [718]2 years ago
8 0
Look at the picture.

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)

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

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)}

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