SOLUTION: Prove that quadrilateral PLUS with vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle but not a square

Algebra ->  Rectangles -> SOLUTION: Prove that quadrilateral PLUS with vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle but not a square      Log On


   

Question 1006745: Prove that quadrilateral PLUS with vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle but not a square
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that quadrilateral PLUS with vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle but not a square

by definition,a rectangle is a quadrilateral that has opposite sides are parallel and of equal length
so, we need to find the distance between vertices which is the length of the sides
if the distance between points P and L is same as the distance between points U and S, then the length of the sides PL and US are same, or PL=US
and if the distance between points U and L is same as the distance between points P and S, then the length of the sides UL and PS are same, or UL=PS
finally, if PL%3C%3EPS and US%3C%3EULthen a quadrilateral is a rectangle
PL
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%286-2%29%5E2+%2B+%283-1%29%5E2%29=+4.47213595499958+


For more on this concept, refer to Distance formula.

and US
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%281-5%29%5E2+%2B+%283-5%29%5E2%29=+4.47213595499958+


For more on this concept, refer to Distance formula.


UL
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%286-5%29%5E2+%2B+%283-5%29%5E2%29=+2.23606797749979+


For more on this concept, refer to Distance formula.

and
PS
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%281-2%29%5E2+%2B+%283-1%29%5E2%29=+2.23606797749979+


For more on this concept, refer to Distance formula.

as you can see, PL=US and UL=PS;so, a quadrilateral is a rectangle