Question

What is the distance in units between `(-74, -4)` and `(21,-4)` on a coordinate plane?

Answer 1

`sqrt9089`

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

Explanation:

Essentially, this is Pythagoras' Theorem in disguise.

As this crude diagram is attempting to show, we have a right-angled triangle, with base of the positive value of `-74-21` and height of `-4-4`. If the hypotenuse is `d`, we can use Pythagoras to find `d`.

`d^2=(-74-21)^2+(-4-4)^2`
`d^2=(-95)^2+(-8)^2`
`d^2=9089`
`d=sqrt9089~~95.34`

I'd recommend keeping your answer as a surd though.

To help with any future questions on this, we can derive a formula using the general case.

The General Case & a simple formula

Let us find the distance between two points `(x_1, y_1)` and `(x_2, y_2)`.

The x distance is equal to `x_2-x_1`. The y distance is equal to `y_2-y_1`. Using Pythagoras:

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

For the future, you can quote and substitute into this formula, but it's definitely worth understanding where it comes from.