Question

What is the distance between (4,2) and (8,5)

Answer 1

5 units

Explanation:

Let's make a (right-angle) triangle out of this! The "bottom" will be made from the x-coordinates, the ''side" out of the y-coordinates, and the hypotenuse (the longest side on a right-angle triangle) is what we're trying to find. 8 - 4 = 4 and 5 - 2 = 3. Therefore, we know the "bottom" is 4 units long and the "side" is 3 units long. To solve for the last side, let's use the Pythagorean theorem, which states that
`a^(2) +b^(2) =c^(2)`, where a and b are the other two sides and c is the hypotenuse:

`3^(2)+ 4^(2) = c^(2)\\9 + 16 = c^(2)\\25 = c^(2)  \\√(25)= \sqrt{c^(2)}\\ 5 = c`

The distance between (4, 2) and (8, 5) is 5 units. You've actually found the most famous Pythagorean triple, (3, 4, 5)!