Question

find the distance between the points (0,-2) and (6,-6)

Answer 1

Answer:

Formular:

$length = \sqrt{ {(x_{1} - x_{2} )}^{2} + {(y_{1} - y_{2} ) }^{2} }$

x1 » 0

x2 » 6

y1 » -2

y2 » -6

$l = \sqrt{ {(0 - 6)}^{2} + {( - 2 - 6)}^{2} } \\ \\ l = \sqrt{ {( - 6)}^{2} + {( - 8)}^{2} } \\ \\ l = \sqrt{36 + 64} \\ \\ l = \sqrt{100}$

for the √100 in surds:

$l = \sqrt{10 \times 10} = \sqrt{ {10}^{2} } = ( {10}^{2} ) {}^{ \frac{1}{2} } \\ \\ { \boxed{ \boxed{distance = 10 \: \: units}}}$

Answer 2

Exact Form:
2√13

Decimal Form:
7.21110255