Question

How do you find the distance between the points (9,-12), (3,-6)?

Answer 1

`6sqrt2`

Explanation:

Using the `color(blue)"distance formula"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(2/2)|)))`
where `(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

The 2 points here are (9 ,-12) and (3 ,-6)

let `(x_1,y_1)=(9,-12)" and " (x_2,y_2)=(3,-6)`

`d=sqrt((3-9)^2+(-6+12)^2)=sqrt(36+36)=sqrt72`

`sqrt72" may be simplified"`

`sqrt72=sqrt(36xx2)=sqrt36xxsqrt2=6sqrt2larr" exact value"`