Question

What is the distance between A(5,-2) and B(-2,4)?

Answer 1

`√(85)`

Explanation:

Let's use the distance formula to solve for the distance between the two given points!

d =
`\sqrt{(x_(2) - x_(1))^2 + (y_(2) - y_(1))^2 }`

Now, we input the points:

(5-(-2) + (-2-4)

(which will equal...)

(7) + (-6)

Now we input the solutions we got here to the distance formula:

`d =\sqrt{(7)^2 + (-6)^2`

(we simplify....)

`7^2 = 49\\(-6)^2 = 36`

input these solutions into the distance formula again...

`√(49 + 36) = √(85)`

85 is not a number that can be square rooted properly, nor does it have any perfect squares available to divide equally.

Therefore, we conclude that the distance between A(5, -2) and B(-2,4) is
`√(85)`.