What is the distance between (15,-10) and (-5,-12)?

distance $d = 2 \sqrt{101}$

$d = 20.09975$

Explanation:

distance formula $d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

Given two points:$\left(15 , - 10\right)$ and $\left(- 5 , - 12\right)$

Let ${P}_{2} \left(15 , - 10\right)$ and ${P}_{1} \left(- 5 , - 12\right)$

so that ${x}_{2} = 15$ and ${y}_{2} = - 10$

also ${x}_{1} = - 5$ and ${y}_{1} = - 12$

Direct substitution to the formula:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

$d = \sqrt{{\left(15 - - 5\right)}^{2} + {\left(- 10 - - 12\right)}^{2}}$

$d = \sqrt{{\left(15 + 5\right)}^{2} + {\left(- 10 + 12\right)}^{2}}$

$d = \sqrt{{\left(20\right)}^{2} + {\left(2\right)}^{2}}$

$d = \sqrt{400 + 4}$

$d = \sqrt{404}$

$d = 2 \sqrt{101}$

$d = 20.09975$

Have a nice day !! from the Philippines..