Question

How do you find the distance between `O(-2, 10)` and `P(-8,3)`?

Answer 1

`sqrt85~~9.22" to 2 dec. places"`

Explanation:

`" find the distance (d) using 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)|)))`

`"let "(x_1,y_1)=(-2,10)" and "(x_2,y_2)=(-8,3)`

`d=sqrt((-8-(-2))^2+(3-10)^2)`

`color(white)(d)=sqrt(36+49)=sqrt85~~9.22`

Answer 2

distance`=sqrt(85)` units `~9.22` units

Explanation:

distance`=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
distance`=sqrt((-8-(-2))^2+(3-10)^2)`
distance`=sqrt((-6)^2+(-7)^2)`
distance`=sqrt(85)` units

I hope that helps :)

Answer 3

Giving an understanding to the distance formula...

Explanation:

Explanation to prior answer.

The '`color(red)("distance"`' formula as stated is just an adaptation of pythagerous' theorem

Let there be two different points `(x_1,y_1) " and " (x_2,y_2)`:

Now drawring dotted lines... We see this is a right angled trianlge, were we can use pythagerouses theorem...