What is the distance between $(7,-22)$ and $(-1,-4)$ ?

Question

1716 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-05T19:07:30

See a solution process below:

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:

$d = sqrt((color(red)(-1) - color(blue)(7))^2 + (color(red)(-4) - color(blue)(-22))^2)$

$d = sqrt((color(red)(-1) - color(blue)(7))^2 + (color(red)(-4) + color(blue)(22))^2)$

$d = sqrt((-8)^2 + 18^2)$

$d = sqrt(64 + 324)$

$d = sqrt(388)$

$d = sqrt(4 * 97)$

$d = sqrt(4)sqrt(97)$

$d = 2sqrt(97)$

Or

$d = 19.698$ rounded to the nearest thousandth.

What is the distance between (7,-22)(7,-22) and (-1,-4)(-1,-4)?