Question

What is the distance between `(1,5)` and `(2,12)`?

Answer 1

`color(white)(xx)5sqrt2`

Explanation:

Let distance be `d`. Then:

`color(white)(xx)d^2=(Deltax)^2+(Deltay)^2color(white)(xxxxxxxxxxx)` (Pythagorous' Theorem)

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

`=>d=sqrt((color(red)2-color(red)1)^2+(color(red)12-color(red)5)^2)`
`color(white)(xxx)=sqrt(color(red)1^2+color(red)7^2)`
`color(white)(xxx)=sqrt(color(red)1+color(red)49)`
`color(white)(xxx)=5sqrt2`