# What is the distance between (5, 6)  and (1, -3) ?

Apr 11, 2016

$4 \sqrt{2}$

#### Explanation:

color(blue)((5,6)and(1,-3)

Use the distance formula

color(brown)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

Note: $d = \mathrm{di}$$s$$t a$$n c e$

Where

color(purple)(x_1=5,x_2=1

color(purple)(y_1=6,y_2=-3

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

$\rightarrow d = \sqrt{{\left(- 4\right)}^{2} + {\left(- 4\right)}^{2}}$

$\rightarrow d = \sqrt{\left(16\right) + \left(16\right)}$

$\rightarrow d = \sqrt{32} = \sqrt{16 \cdot 2}$

color(green)(rArrd=4sqrt2

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