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) About Me  (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:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%285-0%29%5E2+%2B+%281-0%29%5E2%29=+5.09901951359278+


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:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%283-8%29%5E2+%2B+%285-6%29%5E2%29=+5.09901951359278+


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:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%283-0%29%5E2+%2B+%285-0%29%5E2%29=+5.8309518948453+


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:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%288-5%29%5E2+%2B+%286-1%29%5E2%29=+5.8309518948453+


For more on this concept, refer to Distance formula.


these are equations of the lines through given points:
y=0.2x+.........O (0,0) R(5,1)
y=0.2x+%2B+4.4......P(3,5) Q(8,6)
y=%281.66666666666667%29x+............O (0,0) P(3,5)
y=%281.66666666666667%29x+-7.33333333333333.....R(5,1) Q(8,6)


so, OPQR is a parallelogram