Find the distance, to the nearest hundredth, between the given points. P1(6, −1) and P2(−1, −2)

Answer 1

Are you familiar with the equation for distance between two points? It assumes that we're calling our points (x₁,y₁) and (x₂,y₂) and it has you calculate the horizontal distance (x₂-x₁) and the vertical distance (y₂-y₁), and then treats those two distances like the two legs of a right triangle, so that we can use the Pythagorean Theorem to calculate the distance as the hypotenuse. (I can explain this more if you like - just ask!)

The equation looks like this:

Distance = √ [ (x₂-x₁)² + (y₂-y₁)² ].

Notice that you'll do your subtractions to find the differences first, then square the two differences, then add them together, and THEN take the square root of the sum of those two squares. Make sure you're following Order of Operations and the punctuation shown in the equation!

So once we have our equation, and your problem gives you your two points: (x₁,y₁) = (6, -1) and (x₂,y₂) = (-1, -2), we can do our substitutions:

x₁ = 6

y₁ = -1

x₂ = -1

y₂ = -2

and our equation looks like:

√ [ ((-1)-(6))² + ((-2)-(-1))² ]

So just simplify, do your subtraction and squaring and addition and square-root, and you'll have the distance!

Let me know if you get stuck anywhere or want more explanation on why any piece of this problem is done the way that I explained :)