Question

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.

Answer 1

The solution for the problem is:

d(S,P) = √(0-0)^2 + √(b-0)^2
d(S,P) = √b^2
d(S,P) = b

so we know that, 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)

Therefore, the answer is √(a^2 + b^2).