How do you find the distance between (5,1), (5,-6)?

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Answer 1 · 2017-07-01T15:42:26

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:

$d = sqrt((color(red)(5) - color(blue)(5))^2 + (color(red)(-6) - color(blue)(1))^2)$

$d = sqrt(0^2 + (-7)^2)$

$d = sqrt(0 + 49)$

$d = sqrt(49)$

$d = 7$

There is another, simplier process because this is a special case.

Because both the $x$ values are the same we can use this formula:

$d = abs(color(red)(y_2) - color(blue)(y_1))$

$d = abs(color(red)(-6) - color(blue)(1))$

$d = abs(-7)$

$d = 7$