SOLUTION: Find the coordinates of the intersection of the diagonals of parallelogram XYZW with vertices X (3,0), Y (3,8) Z (-2,6), and W (-2,-2). Thank You in Advance, Tutor!

Algebra ->  Angles -> SOLUTION: Find the coordinates of the intersection of the diagonals of parallelogram XYZW with vertices X (3,0), Y (3,8) Z (-2,6), and W (-2,-2). Thank You in Advance, Tutor!       Log On


   

Question 851443: Find the coordinates of the intersection of the diagonals of parallelogram XYZW with vertices X (3,0), Y (3,8) Z (-2,6), and W (-2,-2).
Thank You in Advance, Tutor!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
You can make a graph both to answer and to check; but you can always use points of each pair of opposite corners to form the equations for the lines containing the diagonals, and then solve them as two simultaneous equations. The solution is the intersection point of the diagonals.

XZ
slope %286-0%29%2F%28-2-3%29=-6%2F5.
as if y-mx to get y intercept,
0-%28-6%2F5%293=18%2F5
y=-%286%2F5%29x%2B18%2F5

YW
slope %288-%28-2%29%29%2F%283-%28-2%29%29=2.
y-intercept,+8-2%2A3=2.
y=2x%2B2

FIND INTERSECTION
-
Equating expressions for y, -%286%2F5%29x%2B18%2F5=2x%2B2
-%283%2F5%29x%2B9%2F5=x%2B1
x%2B1=-%283%2F5%29x%2B9%2F5
%288%2F5%29x=4%2F5
highlight%28x=2%29------One of the coordinates
-
y=2x%2B2
y=2%2A2%2B2
highlight%28y=6%29--------Other coordinate

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Find the coordinates of the intersection of the diagonals of parallelogram XYZW with vertices X (3,0), Y (3,8) Z (-2,6), and W (-2,-2).
Thank You in Advance, Tutor! 


Calculate the midpoint of YW. This should be the same as the midpoint of XZ. This will be the intersection

of the 2 diagonals of the //gram.

** Note: Diagonals of a parallelogram BISECT each other.



You can do the check!! 



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