What is the distance between $(2,-6)$ and $(7,4)$ ?

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Answer 1 · 2018-03-11T22:51:37

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:

$d = sqrt((color(red)(7) - color(blue)(2))^2 + (color(red)(4) - color(blue)(-6))^2)$

$d = sqrt((color(red)(7) - color(blue)(2))^2 + (color(red)(4) + color(blue)(6))^2)$

$d = sqrt(5^2 + 10^2)$

$d = sqrt(25 + 100)$

$d = sqrt(125)$

$d = sqrt(25 * 5)$

$d = sqrt(25)sqrt(5)$

$d = 5sqrt(5)$

What is the distance between (2,-6)(2,-6) and (7,4)(7,4)?