How do you find the distance between (10,19), (-13,9)?

Aug 17, 2017

Use ${a}^{2} + {b}^{2} = {c}^{2}$

$c = 25.1$

Explanation:

Let the change in x be ${a}^{2}$
Let the change in y be ${b}^{2}$

The the square root of ${c}^{2}$ = the distance

${a}^{2} = {\left(19 - 9\right)}^{2}$

${a}^{2} = 100$

${b}^{2} = {\left(10 - - 13\right)}^{2}$

${b}^{2} = 529$

$100 + 529 = 629$

$629 = {c}^{2}$

square root of $629 = c$

$c = \sqrt{629}$

$c = 25.1$

Aug 17, 2017

$= 25.08$

Explanation:

The formula for the distance between two points is based on the Theorem of Pythagoras.

|AB| = sqrt((x_2-x_1)^2 + (y_2-y_1)^2))

We have the points $\left(10 , 19\right) \mathmr{and} \left(- 13 , 9\right)$

Distance = $\sqrt{{\left(10 - \left(- 13\right)\right)}^{2} + {\left(19 - 9\right)}^{2}}$

$= \sqrt{{23}^{2} + {10}^{2}}$

$= \sqrt{629}$

$= 25.08$