If the points (x, -1),(3, y),(-2, 3),and (-3, | vedclass

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

Vedclass · Accepted Answer

$x = 2, y = 4$

Vedclass · Answer

(A) Let the vertices of the parallelogram be $A(x, -1)$,$B(3, y)$,$C(-2, 3)$,and $D(-3, -2)$.In a parallelogram,the diagonals bisect each other,meaning the mid-points of the diagonals coincide.The mid-point of diagonal $AC$ is $\left( \frac{x - 2}{2}, \frac{-1 + 3}{2} \right) = \left( \frac{x - 2}{2}, 1 \right)$.The mid-point of diagonal $BD$ is $\left( \frac{3 - 3}{2}, \frac{y - 2}{2} \right) = \left( 0, \frac{y - 2}{2} \right)$.Equating the mid-points: $\frac{x - 2}{2} = 0 \Rightarrow x = 2$.And $1 = \frac{y - 2}{2}$ $\Rightarrow y - 2 = 2$ $\Rightarrow y = 4$.Thus,$x = 2$ and $y = 4$.

If the points $(x, -1)$,$(3, y)$,$(-2, 3)$,and $(-3, -2)$ are the vertices of a parallelogram,then:

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