Answer:
- (5, 4) to origin is √41
- (4, 5) to origin is √41
- √(a^2 +b^2) = √(b^2 +a^2)
Step-by-step explanation:
(b) The distance of point (a, b) from the origin is ...
d = √(a^2 +b^2)
The distance of point (b, a) from the origin is ...
d = √(b^2 +a^2)
The commutative property of addition says these expressions have identical values:
√(a^2 +b^2) = √(b^2 +a^2)
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(a) The distance of interest is ...
d = √(5^2 +4^2) = √(25+16) = √41
It is the same for (4, 5) and (5, 4) as shown above.
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Note that a^2 = (-a)^2, so that any of the points ...
(a, b), (b, a), (-a, b), (b, -a), (a, -b), (-b, a), (-a, -b), (-b, -a)
will all have the same distance from the origin.
