Final answer:
The point on the terminal side of θ = -3π/4 with an x-coordinate of -1 is (-1, -1), as it lies in the third quadrant with both x and y coordinates being negative.
Step-by-step explanation:
To find the point on the terminal side of θ = -3π/4 with an x-coordinate of -1, we first note that θ indicates a reference angle of 3π/4 radians, which corresponds to 135° in standard position. In the Cartesian plane, a point with θ = -3π/4 lies in the third quadrant where both x and y coordinates are negative, and the angles are measured from the positive x-axis in a clockwise direction. Given that the x-coordinate is -1 and we are dealing with a 45°-45°-90° right triangle in the third quadrant (because 3π/4 rad is equivalent to 135°, which makes each acute angle 45°), using the unit circle properties, the y-coordinate will be equal to the x-coordinate in magnitude but negative (since it's in the third quadrant). Therefore, the corresponding y-coordinate for the point is also -1. The point on the terminal side of θ = -3π/4 with an x-coordinate of -1 is (-1, -1).