How do you find the distance between points (-7,8), (3,10)?

Question

3180 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-17T03:43:11

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:

$d = sqrt((color(red)(3) - color(blue)(-7))^2 + (color(red)(10) - color(blue)(8))^2)$

$d = sqrt((color(red)(3) + color(blue)(7))^2 + (color(red)(10) - color(blue)(8))^2)$

$d = sqrt(10^2 + 2^2)$

$d = sqrt(100 + 4)$

$d = sqrt(104)$

$d = sqrt(4 * 26)$

$d = sqrt(4)sqrt(26)$

$d = 2sqrt(26)$

Or

$d = 2 * 5.099$

$d = 10.198$ rounded to the nearest thousandth.