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

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Answer 1 · 2016-04-11T08:57:14

$4 \sqrt{2}$ $4sqrt2$

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

$d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $color(brown)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

Note: $d = d i$ $d=di$ $s$ $s$ $t a$ $ta$ $n c e$ $nce$

Where

$x_{1} = 5, x_{2} = 1$ $color(purple)(x_1=5,x_2=1$

$y_{1} = 6, y_{2} = - 3$ $color(purple)(y_1=6,y_2=-3$

$\to d = \sqrt{{(1 - 5)}^{2} + {(- 3 - 1)}^{2}}$ $rarrd=sqrt((1-5)^2+(-3-1)^2)$

$\to d = \sqrt{{(- 4)}^{2} + {(- 4)}^{2}}$ $rarrd=sqrt((-4)^2+(-4)^2)$

$\to d = \sqrt{(16) + (16)}$ $rarrd=sqrt((16)+(16))$

$\to d = \sqrt{32} = \sqrt{16 \cdot 2}$ $rarrd=sqrt32=sqrt(16*2)$

$\Rightarrow d = 4 \sqrt{2}$ $color(green)(rArrd=4sqrt2$

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