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

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) (Show Source): You can put this solution on YOUR website!
Prove that quadrilateral with vertices P(,), L(,), U(,), and S(,) 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 and is same as the distance between points and , then the length of the sides and are same, or
and if the distance between points and is same as the distance between points and , then the length of the sides and are same, or
finally, if and then a quadrilateral is a rectangle

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.

and

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.

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