# How do you find the distance between the points with the given polar coordinates #P_1(-2.5,pi/8)# and #P_2(-1.75, -(2pi)/5)#?

##### 1 Answer

We get the awesome exact answer

#### Explanation:

There's no magic; we convert to rectangular and do the square root of the sum of squared differences. Let's do it generally and rename the points

That's it.

For the current problem we substitute

The negative magnitudes don't need special handling.

I'm reasonably sure the your teacher will accept some calculator approximation. But here on Socratic you deserve the exact radical form.

I just did this other answer and got

so I won't repeat that here. There's no shortcut to the sine, we simply get

The minus sign comes because we're in the fourth quadrant.

Putting it all together,

Check:

Let's pop the original expression into Alpha . Approximation looks right!