Given point (6,-10) how do you find the distance of the point from the origin, then find the measure of the angle in standard position whose terminal side contains the point?

1 Answer
Mar 26, 2017

See below

Explanation:

To find the distance to the origin you use the distance formula, d=sqrt((x_2-x_1)^2+(y_2-y_1)^2).

Plugging in the coordinates of the given point and the origin, d=sqrt((6-0)^2+("-"10-0)^2)=sqrt136=2sqrt34~~11.7

To find the angle, get a reference angle using tan^("-"1)(|y|/|x|) and then analyze the point to find the correct quadrant.

tan^("-"1)(10/6)~~1.03 and since the point lies on the line below, it is in Quadrant "IV". The value of an angle in Quadrant "IV" is 2pi-alpha where alpha is the reference angle, so the angle for this point is 5.25.

graph{-5x/3 [-1, 23, -11, 1]}