Question

P(−7,2) is rotated 270° (counterclockwise) about the origin. Name the quadrant P′ 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

Answer 1

To find the new coordinates \( P' \) after rotating the point \( P(-7, 2) \) by \( 270^\circ \) counterclockwise about the origin, you can use the rotation formula for a point \( (x, y) \):

\[
(x', y') = (y, -x)
\]

For a \( 270^\circ \) rotation counterclockwise, this means:

\[
(x', y') = (y, -x) = (2, -(-7)) = (2, 7)
\]

Thus, after the rotation, the new coordinates of point \( P' \) are \( (2, 7) \).

Now let's determine the quadrant of the point \( (2, 7) \):

- The x-coordinate is positive (2).
- The y-coordinate is positive (7).

Since both coordinates are positive, point \( P' \) is located in Quadrant I.

So the answer is:

**Option #1: Quadrant I**