What is the distance between #(3 ,( pi)/4 )# and #(-2 , ( pi )/6 )#?

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Answer 1 · 2018-04-03T01:40:26

#color(green)("Distance between the two points : " 4.01 " units"#

First convert the polar coordinates to cartisian. Then calculate the distance using distance formula.

#P(r,theta) -> X(r cos theta, r sin theta)#

#P_1 (3, pi/4) -> A_1 (3 * cos (pi/4), 3 * sin (pi/4)) -> X_1(2.12, 2.12) " (2dp)#

#P_2 (-2, pi/6) -> A_2 (-2 * cos (pi/6), -2 * sin (pi/6)) -> X_2(-1.732, 1)#

Distance between X_1 " and " X_2 is

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

# => sqrt((-1.732-2.12)^2 + (1-2.12)^2#

# " as sine in II quadrant is positive"#

#d = sqrt((-3.852)^2 + (-1.12)^2) = 4.01 " units"#