Three vertices of a kite are (1,8), (1,0), and ( 5 ,6). What is the fourth vertex?
A) (1, -3 )
B) (1, 5 )
C) ( -3 ,6)
D) ( 5 , 4)
E) ( -4 ,6)

Question

Three vertices of a kite are (1,8), (1,0), and ( 5 ,6). What is the fourth vertex? ​
A) (1, -3 )
B) (1, 5 )
C) ( -3 ,6)
D) ( 5 , 4)
E) ( -4 ,6)

Quizplus · Accepted Answer

The fourth vertex of a kite can be found by ensuring the diagonals are perpendicular bisectors of each other. The midpoint of the diagonal between (1,8) and (1,0) is (1,4). For the kite's symmetry, the other diagonal must also pass through this midpoint. The line connecting (5,6) to this midpoint will have a slope that is the negative reciprocal of the slope of the line connecting (1,8) and (1,0), ensuring perpendicularity. The only point that maintains the kite's symmetry and ensures the diagonals bisect each other perpendicularly is (-3,6), making it the fourth vertex.

Three Vertices of a Kite Are (1,8), (1,0), and