How do you find the distance between $(\sqrt{6}, - 6 \sqrt{5})$ $(sqrt6,-6sqrt5)$ , $(2 \sqrt{6}, \sqrt{5})$ $(2sqrt6,sqrt5)$ ?

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Answer 1 · 2017-01-18T20:15:58

When given two points, $(x_{0}, y_{0}) and (x_{1}, y_{1})$ $(x_0,y_0) and (x_1,y_1)$ , the distance, d, between them is:

$d = \sqrt{{(x_{1} - x_{0})}_{1}^{2} + {(y_{1} - y_{0})}_{1}^{2}}$ $d = sqrt((x_1 - x_0)^2 + (y_1 - y_0)^2)$

Given: $(\sqrt{6}, - 6 \sqrt{5}) and (2 \sqrt{6}, \sqrt{5})$ $(sqrt6,-6sqrt5) and (2sqrt6,sqrt5)$

The distance is:

$d = \sqrt{{(2 \sqrt{6} - \sqrt{6})}^{2} + {(\sqrt{5} - - 6 \sqrt{5})}^{2}}$ $d = sqrt((2sqrt6 - sqrt6)^2 + (sqrt5 - -6sqrt5)^2)$

$d = \sqrt{{(\sqrt{6})}^{2} + {(7 \sqrt{5})}^{2}}$ $d = sqrt((sqrt6)^2 + (7sqrt5)^2)$

$d = \sqrt{6 + 245}$ $d = sqrt(6 + 245)$

$d = \sqrt{251}$ $d = sqrt(251)$

$d \approx 15.84$ $d~~ 15.84$

How do you find the distance between (√6,−6√5)(sqrt6,-6sqrt5), (2√6,√5)(2sqrt6,sqrt5)?