Question

What is the distance between `(2,5)` and `(9,1)`?

Answer 1

`color(white)(xx)sqrt65`

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)1-color(red)5)^2+(color(red)9-color(red)2)^2)`
`color(white)(xxx)=sqrt(color(red)4^2+color(red)7^2)`
`color(white)(xxx)=sqrt(color(red)16+color(red)49)`
`color(white)(xxx)=sqrt65`