Question

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?

Answer 1

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]}