Question

Jeff drew the rectangle shown.

The coordinates of point P are (3, –3).
Segment PS measures 9 units in length.
Plot the location of point S on the coordinate plane.

Answer 1

To find the possible locations of point S, we need to determine where point S can be, given that segment PS measures 9 units in length and point P is at (3, -3).

The distance formula helps us find points that have a specific distance from a given point. Specifically, if the distance between points \( P(x_1, y_1) \) and \( S(x_2, y_2) \) is 9 units, we can use the formula for distance:

\[
\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = d
\]

For our case, \( d = 9 \), and point P is (3, -3). Plugging in the coordinates:

\[
\sqrt{(x_2 - 3)^2 + (y_2 + 3)^2} = 9
\]

To eliminate the square root, we square both sides:

\[
(x_2 - 3)^2 + (y_2 + 3)^2 = 81
\]

This equation represents a circle with a center at point P (3, -3) and a radius of 9.

To plot all possible locations of point S, draw a circle centered at the point (3, -3) with a radius of 9 units. Here are some specific points you can calculate and plot on the coordinate plane:

1. To the right of point P (3, -3):
- (3 + 9, -3) = (12, -3)

2. To the left of point P:
- (3 - 9, -3) = (-6, -3)

3. Above point P:
- (3, -3 + 9) = (3, 6)

4. Below point P:
- (3, -3 - 9) = (3, -12)

5. Diagonal points:
- To find other points on the circumference, you can use angles or trigonometric functions. Some calculated points on the circle at specific angles include:
- (3 + 9*cos(45°), -3 + 9*sin(45°)) = (3 + 9*(√2/2), -3 + 9*(√2/2))
- (3 + 9, -3) -> (12, -3)
- (3 - 9, -3) -> (-6, -3)
- (3, -3 + 9) -> (3, 6)
- (3, -3 - 9) -> (3, -12)

Ultimately, you can plot any point that satisfies the distance condition to visually represent point S, anywhere around the circle centered at (3, -3) with a radius of 9.