How do you find the midpoint of each diagonal of the quadrilateral with vertices P(1,3), Q(6,5), R(8,0), and S(3,-2)?

Kevin Charles

Kevin Charles

Answered question

2022-10-22

How do you find the midpoint of each diagonal of the quadrilateral with vertices P(1,3), Q(6,5), R(8,0), and S(3,-2)?

Answer & Explanation

Cagliusov8

Cagliusov8

Beginner2022-10-23Added 15 answers

Step 1
We are given a Quadrilateral with the following Vertices:
P ( 1 , 3 ) , Q ( 6 , 5 ) , R ( 8 , 0 ) , and S ( 3 , - 2 )
The MidPoint Formula for a Line Segment with Vertices ( x 1 , y 1 ) and ( x 2 , y 2 ) :
[ x 1 + x 2 2 , y 1 + y 2 2 ]
Consider the Vertices P ( 1 , 3 ) and R ( 8 , 0 ) of the diagonal PR
L e t ( x 1 , y 1 ) = P ( 1 , 3 )
L e t ( x 2 , y 2 ) = R ( 8 , 0 )
Using the Midpoint formula we can write
[ 1 + 8 2 , 3 + 0 2 ]
[ 9 2 , 3 2 ]
[ 4.5 , 1.5 ]
Step 2
Consider the Vertices Q ( 6 , 5 ) and S ( 3 , - 2 ) of the diagonal QS
L e t ( x 1 , y 1 ) = Q ( 6 , 5 )
L e t ( x 2 , y 2 ) = S ( 3 , - 2 )
Using the Midpoint formula we can write
[ 6 + 3 2 , 5 + ( - 2 ) 2 ]
[ 9 2 , 3 2 ]
[ 4.5 , 1.5 ]
By observing the two Intermediate results 1 and 2, we understand that both the diagonals have the same Midpoint, and hence the given Quadrilateral with four vertices is a Parallelogram.

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