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.
Accepted Solution
A:
d(S,P) = √(0-0)^2 + √(b-0)^2 d(S,P) = √b^2 d(S,P) = b so SP = b
d(P, Q) = √(a-0)^2 + √(b-b)^2 d(P, Q) = √a^2 d(P, Q) = a so PQ = a
SQ = c^2 = a^2 + b^2 SQ = √(a^2 + b^2)
answer the length of one of the diagonals of the rectangle is √(a^2 + b^2)