Three vertices of a parallelogram are (1, 3), | vedclass

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(B) Let the vertices of the parallelogram be $A(1, 3)$,$B(2, 0)$,$C(5, 1)$,and $D(x, y)$.Since the diagonals of a parallelogram bisect each other,the

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$(4, 4)$

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(B) Let the vertices of the parallelogram be $A(1, 3)$,$B(2, 0)$,$C(5, 1)$,and $D(x, y)$.Since the diagonals of a parallelogram bisect each other,the midpoint of diagonal $AC$ is the same as the midpoint of diagonal $BD$.Midpoint of $AC = (\frac{1+5}{2}, \frac{3+1}{2}) = (3, 2)$.Midpoint of $BD = (\frac{2+x}{2}, \frac{0+y}{2})$.Equating the midpoints:$\frac{2+x}{2} = 3$ $\Rightarrow 2+x = 6$ $\Rightarrow x = 4$.$\frac{0+y}{2} = 2 \Rightarrow y = 4$.Thus,the fourth vertex is $(4, 4)$.

Three vertices of a parallelogram are $(1, 3)$,$(2, 0)$,and $(5, 1)$. Find its fourth vertex.

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