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

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Answer 1 · 2016-12-12T01:26:35

Without using calculator, 5.1.

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

$PQ=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$ .

Here, it is

$sqrt((4-3)^2+(2-7)^2)=sqrt 26$

$=(1+25)^(1/2)$

$=25^(1/2)(1+1/25)^(1/2)$

$=5(1+0.04)^(0.5)$

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

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

$=5(1.0198)$

$5.09$ , rounded to24 decimals

$=5.1$ , to the nearest tenth.