Question

How do you find the distance between (-6,-2) and (-7,-5)?

Answer 1

`=sqrt(10)`

Explanation:

We use the distance formula: `sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

Lets label our points for easier classification:
`(color(blue)(-6), color(red)(-2))-> (color(blue)(x_1),color(red)(y_1))`
`(color(blue)(-7), color(red)(-5))-> (color(blue)(x_2),color(red)(y_2))`

Now we can substitute in for the distance formula:
`sqrt(color(blue)((-7-(-6)))^2+color(red)((-5-(-2)))^2)`

`=sqrt(color(blue)((-1))^2+color(red)((-3))^2)`

`=sqrt(color(blue)((1))+color(red)((9)))`

`=sqrt(10)`