SOLUTION: a quadrilateral has how many vertices o (0,0) p(3,5) Q(8,6) and R(5,1) determine whether OPQR is a parallelogram

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Question 659934: a quadrilateral has how many vertices o (0,0) p(3,5) Q(8,6) and R(5,1) determine whether OPQR is a parallelogram
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
vertices O (0,0) P(3,5) Q(8,6) and R(5,1)
determine whether OPQR is a parallelogram
first find the distance between given points:
O (0,0) R(5,1)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:



Thus in our case, the required distance is



For more on this concept, refer to Distance formula.


P(3,5) Q(8,6)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:



Thus in our case, the required distance is



For more on this concept, refer to Distance formula.


O (0,0) P(3,5)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:



Thus in our case, the required distance is



For more on this concept, refer to Distance formula.


R(5,1) Q(8,6)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:



Thus in our case, the required distance is



For more on this concept, refer to Distance formula.


these are equations of the lines through given points:
.........O (0,0) R(5,1)
......P(3,5) Q(8,6)
............O (0,0) P(3,5)
.....R(5,1) Q(8,6)


so, OPQR a parallelogram

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