Answer:
5 units
Step-by-step 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 [tex]a^{2} +b^{2} =c^{2}[/tex], where a and b are the other two sides and c is the hypotenuse:
[tex]3^{2}+ 4^{2} = c^{2}\\9 + 16 = c^{2}\\25 = c^{2} \\\sqrt{25}= \sqrt{c^{2}}\\ 5 = c[/tex]
The distance between (4, 2) and (8, 5) is 5 units. You've actually found the most famous Pythagorean triple, (3, 4, 5)!
