Question

What is the distance between `(-9 ,( 17 )/12 )` and `(-2 ,(-7 pi )/4 )`?

Answer 1

I got: `d~~8.103` to 3 decimal places

Perhaps some one else can spot an easier way of working it out!

Explanation:

`color(blue)("Assumption: We are looking at the shortest distance between the two Cartesian points.")`
`color(blue)("Which is a strait line.")`

`color(magenta)("However, the" (-7pi)/4"implies Polar Coordinate system. It is not stated that this is the case!!!")`

Ant two points on a strait line graph can be viewed as forming a right triangle. Unless it is of the forms`x=n" or y=p` where n and p are some constant.

So we are looking at `("difference in y-axis")/("difference in x-axis")`

That is `(x_2-x_1)/(y_2-y_1)`

Let `(x_1,y_1)->(-9,17/12)`

Let `(x_2,y_2)->(-2,(-7pi)/4)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using Pythagoras

Let the distance between the points be d then

`d^2= (x_2-x_1)^2+(y_2-y_1)^2`

`d^2=[color(white)(1/2)(-2)-(-9)]^2+[(-7pi)/4-17/12]^2`

`d^2=7^2+( (17-21pi )/12)^2`

`d=sqrt( 49 + (2398.398)/144)color(white)(...)` to 3 decimal places

`d~~8.103` to 3 decimal places