Choose the point on the terminal side of -210 degrees a) (-1, 1) b) (-1, square root of three ) c) ( square root of three , -1) d) ( negative square root of three , 1)

To find in which quadrant -210 lies, we subtract the angle from 360 degree.
Thus, 360 -210 = 150 degree (positive angle)
Thus, -210 degrees will be +150 degree in will lie in the second quadrant.
Now, in the 2nd quadrant, x-values are negative and y-values are positive.
Now, slope, = tan 150

So, slope= -1/(square root 3)

Now, we will find the coordinate, which gives this slope.

Also, slope= y-value/x-value

Only option (d) satisfies this condition.So,point (d) lies on the terminal side of the angle -210 degrees.