Question

P (-7,2) is rotated (counterclockwise) about the origin. Name the quadrant is located in.
Enter the option number that corresponds to your answer.
Option #1: Quadrant I
Option #2: Quadrant II
Option #3: Quadrant III
Option #4: Quadrant IV
(1 point)

Answer 1

To determine the quadrant in which point P (-7, 2) will be located after being rotated counterclockwise about the origin, we'll analyze the rotation of the point.

The original coordinates P (-7, 2) indicate:
- x = -7 (which is negative, placing it on the left side of the y-axis)
- y = 2 (which is positive, placing it above the x-axis)

When you rotate a point counterclockwise about the origin, the transformation of the coordinates can be described using a 90-degree rotation as follows:
- A point (x, y) rotates to (-y, x).

For our point P (-7, 2):
1. Applying the 90-degree counterclockwise rotation:
- New x-coordinate = -y = -2
- New y-coordinate = x = -7
Thus, the new coordinates after rotation are (-2, -7).

Now we can determine which quadrant the point (-2, -7) is located in:
- The x-coordinate is -2 (negative), placing it on the left side of the y-axis.
- The y-coordinate is -7 (negative), placing it below the x-axis.

The point (-2, -7) is located in Quadrant III.

Therefore, the answer corresponds to Option #3: Quadrant III.