Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. she starts by assigning coordinates to a rectangle as shown. then she uses the coordinates to write and simplify expressions for the lengths of the diagonals. what is the length of one of the diagonals of the rectangle? enter an expression in the box for the length of the diagonal.

The length of a line with known end point coordinates is given by Pythagoras's theorem

The expression for the length of the diagonal , is

The expression for the length of the diagonal  , is

Reason:

The given coordinates of the vertices are; P(0, b), Q(a, b), R(a, 0), and S(0, 0)

The lengths of the diagonals are given by the equation for finding the length, l, of a line given the coordinates which is

Where:

(x₁, y₁) = P(0, b), and (x₂, y₂) = R(a, 0), we get;

Where:

(x₁, y₁) = Q(a, b), and (x₂, y₂) = S(0, 0), we get;

Therefore,

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