# How do you find the distance between the points (5, 1/4), (3,4)?

May 24, 2018

$\frac{17}{4} = 4.25$

#### Explanation:

$\text{to calculate the distance use the "color(blue)"distance formula}$

•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

$\text{let "(x_1,y_1)=(5,1/4)" and } \left({x}_{2} , {y}_{2}\right) = \left(3 , 4\right)$

$d = \sqrt{{\left(3 - 5\right)}^{2} + {\left(4 - \frac{1}{4}\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{{\left(- 2\right)}^{2} + {\left(\frac{15}{4}\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{4 + \frac{225}{16}}$

$\textcolor{w h i t e}{d} = \sqrt{\frac{64}{16} + \frac{225}{16}}$

$\textcolor{w h i t e}{d} = \sqrt{\frac{289}{16}} = \frac{17}{4} = 4.25$

May 24, 2018

$\frac{17}{4}$

#### Explanation:

$\mathrm{di} s t \left(\left[a , b\right] , \left(x , y\right)\right) = \sqrt{{\left(x - a\right)}^{2} + {\left(y - b\right)}^{2}}$

${d}^{2} = {\left(5 - 3\right)}^{2} + {\left(4 - \frac{1}{4}\right)}^{2}$

${d}^{2} = 4 + \frac{225}{16}$

$d = \sqrt{\frac{289}{16}}$