The set of points (4, 3), (7, 3), (4, 0), and (7, 0) identifies the vertices of a quadrilateral. which is the most specific description to tell which figure the points form?

The given points are the vertices of a rectangle.

Step-by-step explanation:

Distance formula

d = √(x₂-x₁)² + (y₂-y₁)²

It is given that, The  set of points (4, 3), (7, 3), (4, 0), and (7, 0) .

Let ABCD be the quadrilateral with,

A(4, 3), B(7, 3), C(4, 0), and D(7, 0).

To find each side of ABCD

A(4, 3), B(7, 3), C(4, 0), and D(7, 0).

AB = √(x₂-x₁)² + (y₂-y₁)²  = √[(7-4)² + (3-3)²] = 3

BC = √(x₂-x₁)² + (y₂-y₁)²  = √[(4-7)² + (0-3)²] =  √18 =  3√3

CD = √(x₂-x₁)² + (y₂-y₁)²  = √[(7-4)² + (0-0)²] = 3

AD = √(x₂-x₁)² + (y₂-y₁)²  = √[(7-4)² + (0-3)]² =  √18 =  3√3

To find the diagonals

AC = √(x₂-x₁)² + (y₂-y₁)²  = √[(4-4)² + (0-3)² ]= 3

BD = √(x₂-x₁)² + (y₂-y₁)²  = √[(7-7)² + (0-3)² ]= 3

Conclusion

From the above result we can see that,

AB = CD ,BC = AD and diagonals AC = BD

Opposite sides are equal and diagonals are equal.

Therefore ABCD is a rectangular.