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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Rectangles

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Exercise 57 Page 511

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

(2.5,0.5)

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 DB. Let's substitute the coordinates of D and B into the Midpoint Formula to find the midpoint of DB.

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

SubstitutePoints

Substitute ( -1, - 1) & ( 6, 2)

( -1+ 6/2, - 1+ 2/2 )

Add and subtract terms

( 5/2, 1/2 )

Calculate quotient

(2.5,0.5)

The midpoint of DB is (2.5,0.5). Consequently, these are the coordinates of the intersection of the diagonals of the parallelogram ABCD.

Subchapter links

Exercises p.508-511