SOLUTION: The vertices of a kite are A (-3,1), B(0,5), C(4,2) and D(2, -9). Determine the lengths of the four sides of the kite. What do you notice? Determine the slopes of the dia

Question 1179468: The vertices of a kite are A (-3,1), B(0,5), C(4,2) and D(2, -9).
Determine the lengths of the four sides of the kite. What do you notice?
Determine the slopes of the diagonals (from one corner to the other corner)
What do you notice?
Find the midpoint of the diagonal AC.
Find the equation of the diagonal BD.
Show the midpoint of AC lies on the equation of a line though BD.
Analyze the previous calculations and list as many properties of a kite as you can.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

The vertices of a kite are
A (,)
B(,)
C(,)
D(,)

Determine the lengths of the four sides of the kite. What do you notice?
the length of is:

the length of is:

I noticed that the length of is equal to the length of , and the length of is equal to the length of

Determine the slopes of the diagonals (from one corner to the other corner)
What do you notice?
the diagonal lie on a line that contains vertices and
slope is .......use A (,) and C(,)

and lie on a line that contains vertices B(,) and D(,)

=>I have noticed that slopes are negative reciprocal to each other which means the diagonals are perpendicular to each other

Find the midpoint of the diagonal AC.
A (,) and C(,)
=(,)
=(,)
Find the equation of the diagonal .
use and point B(,), plug it in poit slope formula

Show the midpoint of AC lies on the equation of a line though BD.
the midpoint of AC is =(,)
......substitute coordinates of the midpoint

-> same, so the midpoint of lies on the equation of a line though

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