Question

HELP PLS ASAP! giving 25 points a) Show that the points (5,4) and (4,5) are the same distance from the origin. The distance from the point (5,4) to the origin is: The distance from the point (4,5) is: b) Show that the points (a,b) to the origin is: The distance from the point (b,a) to the origin is: thanks!!

Answer 1

• (5, 4) to origin is √41
• (4, 5) to origin is √41
• √(a^2 +b^2) = √(b^2 +a^2)

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.