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

1 Answer
Dec 12, 2016

Answer:

Without using calculator, 5.1.

Explanation:

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.