Question

How do you find the distance between (6,-12) and (12,8)?

Answer 1

`sqrt436~~20.88" to 2 dec. places"`

Explanation:

`"to calculate the distance use the "color(blue)"distance formula"`

`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 " (6,-12)" and " (12,8)`

`"let " (x_1,y_1)=(6,-12)" and " (x_2,y_2)=(12,8)`

`d=sqrt((12-6)^2+(8-(-12))^2)`

`color(white)(d)=sqrt(6^2+20^2)`

`color(white)(d)=sqrt436~~20.88" to 2 decimal places"`

Answer 2

`2sqrt 109 ~=20.88`

Explanation:

Use the formula `sqrt((y_2-y_1)^2+(x_2-x_1)^2)`

`y_1 = 8`
`y_2 = -12`
`x_1 = 12`
`x_2 = 6`

`= sqrt((8--12)^2+(12-6)^2)`

`= 2sqrt 109 ~=20.88`