If three vertices of a square are (-4, 3),(10 | vedclass

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Question

(B) Let the vertices of the square be $A(-4, 3)$,$B(10, 5)$,$C(12, -9)$,and $D(x, y)$.In a square,the diagonals bisect each other at the same midpoint

Vedclass · Accepted Answer

$(-2, -11)$

Vedclass · Answer

(B) Let the vertices of the square be $A(-4, 3)$,$B(10, 5)$,$C(12, -9)$,and $D(x, y)$.In a square,the diagonals bisect each other at the same midpoint.Let the diagonals be $AC$ and $BD$.The midpoint of $AC = ((-4 + 12)/2, (3 - 9)/2) = (8/2, -6/2) = (4, -3)$.The midpoint of $BD = ((10 + x)/2, (5 + y)/2)$.Equating the midpoints: $(10 + x)/2 = 4 \implies 10 + x = 8 \implies x = -2$.$(5 + y)/2 = -3 \implies 5 + y = -6 \implies y = -11$.Thus,the fourth vertex is $(-2, -11)$.

If three vertices of a square are $(-4, 3)$,$(10, 5)$,and $(12, -9)$,then find the fourth vertex of the square.

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