Question

How do you find the distance between (7,2), (-5,7)?

Answer 1

`13`

Explanation:

The easiest way to find the distance between two points is to use the distance formula:
`d = sqrt((x_2 - x_1)^2 + (y_2-y_1)^2`

It looks really complicated and confusing, but I'll help you through it.

Remember that points are in the form: `(x,y)`.

• I am going to call `(7,2)` Point 1, so:
  `x_1 = 7`
  `y_1 = 2`
• I'm going to call `(-5,7)` Point 2, so:
  `x_2 = -5`
  `y_2 = 7`

Now all we have to do is substitute those into the equation and solve. Here goes nothing:

`d = sqrt((x_2 - x_1)^2 + (y_2-y_1)^2`

`d = sqrt((-5 - 7)^2 + (7-2)^2`

`d = sqrt((-12)^2 + (5)^2`

`d = sqrt(144 + 25`

`d = sqrt169`

`d = 13`

So the distance between `(7,2)` and `(-5,7)` is `13`.