Question

What is the distance between `(31,-201)` and `(28,-209)`?

Answer 1

See a solution process below:

Explanation:

The formula for calculating the distance between two points is:

`d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)`

Substituting the values from the points in the problem gives:

`d = sqrt((color(red)(28) - color(blue)(31))^2 + (color(red)(-209) - color(blue)(-201))^2)`

`d = sqrt((color(red)(28) - color(blue)(31))^2 + (color(red)(-209) + color(blue)(201))^2)`

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

`d = sqrt(9 + 64)`

`d = sqrt(73)`

Or

`d = 8.544` rounded to the nearest thousandth.

Answer 2

`color(blue)(8.544`

Explanation:

`:.y-y=(-201)-(-209)=8=opposite`

`:.x-x=31-28=3=adjacent`

`:.8/3=tantheta=2.666666667=69°26'38''`

hypotenuse=distance

Distance`:.=sectheta xx 3`

Distance`:.=sec69°26'38'' xx 3`

Distance`:.=2.848001248 xx 3=8.544003745`

`:.color(blue)(=8.544` to 3 decimals