Question

What is the exact distance between
`(10, 6)` and
`(1, -4)`?

Answer 1

`\boxed{√(181)}`

Explanation:

The formula for the distance between two points is

`d = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)}`

x₂ - x₁ = 10 - 1 = 9

y₂ - y₁ = 6 - (-4) = 10

The formula, in effect, creates a right triangle, so we can use the Pythagorean theorem to calculate the distance.

`\begin{array}{rcl}d & = &\sqrt{9^(2) + 10^(2)}\\& = & √(81 + 100)\\& = & √(181)\\\end{array}\\\text{181 is a prime number. It has no factors that allow us to simplify its square root.}\\\text{The exact distance between the points is $\boxed{\mathbf{√(181)}}$}`