Question

Point Q is located at minus, 9−9. Points R and S are each 8 units away from Point Q. Where are R and S located?

Answer 1

Point Q is at the coordinates (-9, -9).

To find points R and S, which are each 8 units away from point Q, we can use the concept of a circle with a radius of 8 centered at point Q.

The equation of a circle in a coordinate system can be expressed as:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

where \((h, k)\) is the center of the circle and \(r\) is the radius. For our case:
- \(h = -9\)
- \(k = -9\)
- \(r = 8\)

The equation becomes:

\[
(x + 9)^2 + (y + 9)^2 = 8^2
\]

Which simplifies to:

\[
(x + 9)^2 + (y + 9)^2 = 64
\]

To find specific points R and S, we can find points along the circle by choosing values for \(x\) or \(y\) and then solving for the other variable.

### Example Points:

1. **Horizontal Movement:**
If we move 8 units directly to the right (positive x-direction):
- \(x = -9 + 8 = -1\)
- \(y = -9\)
- Thus, point R = (-1, -9)

If we move 8 units directly to the left (negative x-direction):
- \(x = -9 - 8 = -17\)
- \(y = -9\)
- Thus, point S = (-17, -9)

2. **Vertical Movement:**
If we move 8 units directly up (positive y-direction):
- \(x = -9\)
- \(y = -9 + 8 = -1\)
- Thus, point R can also be (-9, -1)

If we move 8 units directly down (negative y-direction):
- \(x = -9\)
- \(y = -9 - 8 = -17\)
- Thus, point S can also be (-9, -17)

### Summary of Possible Points:
- Two points could be:
1. R = (-1, -9)
2. S = (-17, -9)

- Alternatively:
1. R = (-9, -1)
2. S = (-9, -17)

Thus, points R and S can be located at any of these combinations based on their directions from Q.