Question

Suppose you use the Pythagorean theorem to find the distance between the ordered pairs shown. When you form the right triangle, what is the length of its LONGEST leg?

Answer 1

`√(31)`

The triangles lengths are: 4, 5, x

Pythagorean theorem:
`a^(2)` +
`b^(2)` =
`c^(2)`

------>
`4^(2)` +
`5^(2)` =
`x^(2)`

----------> 16 + 25 =
`x^(2)`

--------------> 31 =
`x^(2)`

------------------> x =
`√(31)`

`√(31)` is the hypotenuse, so it's the longest side.