Final answer:
To plot the point P(-6√2, -6√2), plot its x-coordinate -6√2 along the x-axis and its y-coordinate -6√2 along the y-axis. To show that the distance of point P to the origin is invariant under rotations of the coordinate system, calculate the distance between P and the origin using the distance formula.
Step-by-step explanation:
To plot the point P(-6√2, -6√2), we plot its x-coordinate -6√2 along the x-axis and its y-coordinate -6√2 along the y-axis. The point P will be located at the intersection of these two lines.
To show that the distance of point P to the origin is invariant under rotations of the coordinate system, we calculate the distance between P and the origin. The distance between two points (x1, y1) and (x2, y2) in the coordinate plane can be found using the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
Calculating the distance between P(-6√2, -6√2) and the origin (0, 0), we have:
d = √((-6√2 - 0)² + (-6√2 - 0)²) = √(72 + 72) = √144 = 12
The distance between P and the origin is 12, which remains the same regardless of the orientation of the coordinate system. Therefore, the distance of point P to the origin is invariant under rotations of the coordinate system.