Question

Find the distance between (0, -8) and (3, -2). Express your answer as a simplified radical, if possible.

Answer 1

3√5
PLEASE DON’T USE DISTANCE FORMULA. It makes me mad how so many teachers still teach it and the students are blindly following them. Use Pythagorean theorem.
1. Find distance between the two x’s from the two points. That would be 3.
2. Now for the y’s. That would be 6
3. Pythagorean theorem is a^2+b^2=c^2 then square root of both sides. You want to find c.
4. Now plug in your distance between x and y into a and b.
5. (3)^2+(6)^2=45. But don’t forget the square root over it. So it’s really square root of 45
6. Square root of 45 is your distance between those two points. Simplify that you get 3√5

Answer 2

`d = 3\sqrt5`

Explanation:

We can find the shortest distance between two points
`(a, b)` and
`(c, d)` using the distance formula:

`d = √((c-a)^2+(d-b)^2)`

From the given points
`(0, -8)` and
`(3, -2)`, we can identify the following variable values:

• 
  `a = 0`
• 
  `b = -8`
• 
  `c = 3`
• 
  `d=-2`

Plugging these into the formula and solving for distance:

`d = √((3-0)^2+((-2)-(-8))^2)`

`d = √(3^2 + (-2 + 8)^2)`

`d = √(3^2 + 6^2)`

`d = √(9 + 36)`

`d = √(45)`

Finally, we can express the distance in simplest radical form by factoring the number under the square root and taking out any perfect squares.

`d = √(9 \cdot 5)`

`\boxed{d = 3\sqrt5}`

Further Note

The distance formula is just a manipulation of the Pythagorean Theorem. It basically models a right triangle with the two given points as vertices and solves for the hypotenuse.