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

1 Answer
Jan 7, 2017

sqrt (85-42sqrt3)

Explanation:

Let P be the point (-6, pi/3) , which is (r, theta) in polar coordinates, and Q be the point (7, pi/2) like wise in the polar coordinates. To plot the point P, move along the ray making an angle theta=pi/3 with positive x-axis at the origin and extend the ray backwards in the IIIrd quadrant. Since r is negative, length 6 units would be measured along the ray in the third quadrant. As shown in the calculation below the cartesean coordinates of P would be (-3, -3sqrt3).

Similarly the cartesean coordinates of Q would be (0,7).

The distance PQ would be sqrt ((3-0)^2 +(3sqrt3 -7)^2)

= sqrt (9+27 +49 -42sqrt3)

=sqrt (85-42sqrt3)

enter image source here