Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. she starts by assigning coordinates

Question

4 years ago

9

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.

Mathematics

1 answer:

storchak [24] · Answer 1 · 2022-01-15T01:23:18+03:00

The solution for the problem is:

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

</span>

so we know that<span>, SP = b</span>

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).