Find the distance between the points (2, 1) and (9,0).

Mathematics

1 answer:

notka56 [123]2 years ago

5 0

Answer:

5√2 units

Step-by-step explanation:

Use distance formulae to find out the distance.

$\rm \: Distance = \sqrt{(x_2-x_1) {}^{2} +(y_2-y_1) {}^{2} }$

ATQ,

$\rm \: (x_2,x_1) = (9,2)$
$\rm (y_2,y_1) = (0,1)$

Substituting them on the formulae,we obtain

$\rm \: Distance \: D = \sqrt{(9 - 2) {}^{2} + (0 - 1) {}^{2} }$
$\rm \: Distance \: D = \sqrt{7 {}^{2} - 1 {}^{2} }$
$\rm \: Distance \; D = \sqrt{49 + (- 1 \times - 1)}$
$\rm Distance \: D = \sqrt{49 + 1}$
$\rm Distance\; D = \sqrt{50}$
$\boxed{ \rm \: Distance \: D = 5 \sqrt{2} \: units}$

You might be interested in

Write each percent as a fraction in simplest form and as a decimal to the nearest hundredth.

Vladimir79 [104]

$p\%=\dfrac{p}{100}=p:100$

$1.\ 30\%=\dfrac{30}{100}=\dfrac{3}{10}\\\\30\%=30:100=0.3\\\\2.\ 42\%=\dfrac{42}{100}=\dfrac{42:2}{100:2}=\dfrac{21}{50}\\\\42\%=42:100=0.42\\\\3.\ 18\%=\dfrac{18}{100}=\dfrac{18:2}{100:2}=\dfrac{9}{50}\\\\18\%=18:100=0.18$

$4.\ 35\%=\dfrac{35}{100}=\dfrac{35:5}{100:5}=\dfrac{7}{20}\\\\35\%=35:100=0.35\\\\5.\ 100\%=\dfrac{100}{100}=\dfrac{1}{1}=1\\\\100\%=100:100=1.0\\\\6.\ 29\%=\dfrac{29}{100}\\\\29\%=29:100=0.29$

$7.\ 56\%=\dfrac{56}{100}=\dfrac{56:4}{100:4}=\dfrac{14}{25}\\\\56\%=56:100=0.56\\\\8.\ 66\dfrac{2}{3}\%=\dfrac{66\cdot3+2}{3}\%=\dfrac{200}{3}\%\\\\\dfrac{200}{3}\%=\dfrac{\frac{200}{3}}{100}=\dfrac{200}{3\cdot100}=\dfrac{2}{3}\\\\\dfrac{200}{3}\%=\dfrac{200}{3}:100=66.666...:100=0.666...\approx0.67\\\\9.\ 25\%=\dfrac{25}{100}=\dfrac{25:25}{100:25}=\dfrac{1}{4}\\\\25\%=25:100=0.25$