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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Tests for Parallelograms
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Exercise 50 Page 503

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

(1,0.5 )

Practice makes perfect

Let's plot the given points and draw the parallelogram with its diagonals on a coordinate plane.

The diagonals of a parallelogram will always bisect each other. Therefore, to find the coordinates of the intersection of the diagonals, we can find the midpoint of either AC or BD. Let's substitute the coordinates of A and C into the Midpoint Formula to find the midpoint of AC.

( x_1+x_2/2, y_1+y_2/2 )
SubstitutePoints

Substitute ( - 3, 5) & ( 5, - 4)

( -3 + 5/2, 5+( - 4)/2 )
AddNeg

a+(- b)=a-b

( -3+5/2, 5-4/2 )
AddSubTerms

Add and subtract terms

( 2/2, 1/2 )
CalcQuot

Calculate quotient

( 1, 1/2 )
WriteDec

Write as a decimal

( 1, 0.5 )

The midpoint of AC is (1,0.5). Consequently, these are the coordinates of the intersection of the diagonals of the parallelogram ABCD.

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