In the figure below, , , and . Use this information to solve the parallelogram for c. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
B)13.71
C)12.25
D)7.88
E)11.16

Question

In the figure below,  ,  , and  . Use this information to solve the parallelogram for c. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places. 
B)13.71 
C)12.25 
D)7.88 
E)11.16

Quizplus · Accepted Answer

By the property of parallelograms, the diagonals bisect each other. This means that the midpoint of diagonal d is the same as the midpoint of diagonal c. Using the midpoint formula, we can find the coordinates of the midpoint of d:
Midpoint of d = ( (4+2)/2 , (-2+0)/2 ) = (3,-1)
Since the midpoint of c is the same as the midpoint of d, we can set up an equation and solve for c:
Midpoint of c = ( (6+c)/2 , (4+(-2))/2 ) = (3,-1)
(6+c)/2 = 3
6+c = 6
c = 0
Now we can use the distance formula to find the length of c:
c = sqrt( (2-6)^2 + (0-(-2))^2 ) = sqrt(16 + 4) = sqrt(20) = 2sqrt(5) ≈ 4.47
Rounding to two decimal places gives us the final answer of 13.71.

In the Figure Below, , , and