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ella
1 month ago
13

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.

Mathematics
2 answers:
Zina [12.3K]1 month ago
5 0

Response:

The accurate response is  √a^2 + b^2 I took the test and this is the correct answer I assure you

Detailed explanation:


Svet_ta [12.7K]1 month ago
4 0
d(S,P) = √(0-0)^2 + √(b-0)^2
d(S,P) = √b^2
d(S,P) = b
therefore
SP = b

d(P, Q) = √(a-0)^2 + √(b-b)^2
d(P, Q) = √a^2
d(P, Q) = a
thus
PQ = a 

SQ = c^2 = a^2 + b^2
SQ = √(a^2 + b^2)

response
 the length of one diagonal of the rectangle equals √(a^2 + b^2)
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