Question

What is the distance between `(3 ,(7 pi)/6 )` and `(-2 , (5 pi )/12 )`?

Answer 1

`sqrt((4900 + (81pi^2))/196)` units

Explanation:

let (`x_1,y_1`)= (3, `7pi`/6) and (`x_2,y_2`)= (-2, `5pi`/12)
Now using the distance formula,
distance = `sqrt((x_2-x_1)^2 + (y_2-y_1)^2)`
= `sqrt((-2-3)^2 + (5pi/12-7pi/6)^2)`
=`sqrt((-5)^2 + ((5pi-14pi)/14)^2`
= `sqrt(25 + ((-9pi)/14)^2`
= `sqrt(25 + (81pi^2)/196)`
= `sqrt((4900 + (81pi^2))/196)` units
you can put the value of `pi` as 22/7 and use the calculator to find the distance.