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

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

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

$" as sine in II quadrant is positive"$

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

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