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[tex]$U(5,3)$[/tex], [tex]$J(5,-3)$[/tex], and [tex]$L(-4,3)$[/tex] are three vertices of rectangle [tex]$UJKL$[/tex]. What are the coordinates of the fourth vertex, [tex]$K$[/tex], of rectangle [tex]$UJKL$[/tex]?

A. [tex]$(-4,-3)$[/tex]
B. [tex]$(5,3)$[/tex]
C. [tex]$(5,-3)$[/tex]
D. [tex]$(-4,3)$[/tex]



Answer :

GinnyAnswer
To determine the coordinates of the fourth vertex [tex]\( K \)[/tex] of rectangle [tex]\( UKL \)[/tex], let's analyze the given vertices [tex]\( I(5, 3) \)[/tex], [tex]\( J(5, -3) \)[/tex], and [tex]\( L(-4, 3) \)[/tex].

1. Identify the common x and y coordinates:
- Both [tex]\( I \)[/tex] and [tex]\( J \)[/tex] share the same x-coordinate, [tex]\( x = 5 \)[/tex], but different y-coordinates, [tex]\( y = 3 \)[/tex] for [tex]\( I \)[/tex] and [tex]\( y = -3 \)[/tex] for [tex]\( J \)[/tex].
- [tex]\( I \)[/tex] and [tex]\( L \)[/tex] share the same y-coordinate, [tex]\( y = 3 \)[/tex], but different x-coordinates, [tex]\( x = 5 \)[/tex] for [tex]\( I \)[/tex] and [tex]\( x = -4 \)[/tex] for [tex]\( L \)[/tex].

2. Determine the remaining coordinates:
- Since [tex]\( I \)[/tex] and [tex]\( J \)[/tex] share the x-coordinate, the fourth vertex [tex]\( K \)[/tex] must also share the x-coordinate with [tex]\( L \)[/tex], which is [tex]\( x = -4 \)[/tex].
- Since [tex]\( I \)[/tex] and [tex]\( L \)[/tex] share the y-coordinate, [tex]\( K \)[/tex] must also share the y-coordinate with [tex]\( J \)[/tex], which is [tex]\( y = -3 \)[/tex].

Thus, the coordinates of the fourth vertex [tex]\( K \)[/tex] are [tex]\( (-4, -3) \)[/tex].

The correct answer is:
A. [tex]\( (-4, -3) \)[/tex]

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