What is the distance between $(2, - 14)$ $(2,-14)$ and $(- 4, 5)$ $(-4,5)$ ?

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Answer 1 · 2016-03-05T23:27:52

I assume that you know the distance formula (square root of sum of corresponding coordinates squared)

$\sqrt{{(a - b)}^{2} + {(c - d)}^{2}}$ $sqrt((a-b)^2 + (c-d)^2$

We can just plug in the corresponding values into the formula

$\sqrt{{(2 - (- 4))}^{2} + {(- 14 - 5)}^{2}}$ $sqrt((2-(-4))^2 + (-14-5)^2$

$\sqrt{{(6)}^{2} + {(- 19)}^{2}}$ $sqrt((6)^2 + (-19)^2)$

This becomes $\sqrt{36 + 361}$ $sqrt(36+361)$

Which is $\sqrt{397}$ $sqrt(397)$

This cannot be simplified further, so we are done.

What is the distance between (2,−14)(2,-14) and (−4,5)(-4,5)?