How do you find the distance between points P(3, 7) and P(4, 2) to the nearest tenth?

Dec 12, 2016

Without using calculator, 5.1.

Explanation:

The distance between P(x_1m y_1) and Q(x_2, y_2),

$P Q = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$.

Here, it is

$\sqrt{{\left(4 - 3\right)}^{2} + {\left(2 - 7\right)}^{2}} = \sqrt{26}$

$= {\left(1 + 25\right)}^{\frac{1}{2}}$

$= {25}^{\frac{1}{2}} {\left(1 + \frac{1}{25}\right)}^{\frac{1}{2}}$

$= 5 {\left(1 + 0.04\right)}^{0.5}$

=5(1+(1/2)(0.04)+((1/2)(1/2-1))/(2!)(0.04^2)+((1/2)(1/2-1)(1/2-2))/(3!)(0.04)^3+..), using binomial expansion

=5(1+0.02-0.0002+000004 + smaller value)#

$= 5 \left(1.0198\right)$

$5.09$, rounded to24 decimals

$= 5.1$, to the nearest tenth.