SOLUTION: If A (1,-2),B(3,6)And C(5,10) Are The Three Vertices Of Aparallelogram, Find Its 4th Vertex D.Also,Find The Angle Between The Diagonals AC And BD.

Algebra ->  Parallelograms -> SOLUTION: If A (1,-2),B(3,6)And C(5,10) Are The Three Vertices Of Aparallelogram, Find Its 4th Vertex D.Also,Find The Angle Between The Diagonals AC And BD.       Log On


   

Question 388240: If A (1,-2),B(3,6)And C(5,10) Are The Three Vertices Of Aparallelogram, Find Its 4th Vertex D.Also,Find The Angle Between The Diagonals AC And BD.



Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

To go from C to D, you move over 2 and up 4.
To keep it a parallelogram, move that same distance from A to D.
D:(1,-2)+(2,4)=(3,2)

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From the diagram,
tan%28XAC%29=%2810-%28-2%29%29%2F%285-1%29=12%2F4=3
XAC=63.4degrees
Also,
XBD=90degrees, since x%5BB%5D=x%5BD%5D
So then the angle between the diagonals, theta, is,
theta=90-71.6
highlight%28theta=18.4%29degrees