To find the coordinates of points A' and B', we first need to clarify what is meant by these points. If A' and B' refer to the reflection of points A and B across some line or point, please specify the line or point of reflection.
However, if you are interested in finding the midpoint, slope, or distance between points A(1, 2) and B(-2, -1), we can proceed with that.
1. Midpoint (M) of Line AB
The midpoint M of points A(x₁, y₁) and B(x₂, y₂) is given by the formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Substituting the coordinates of points A and B: \[ M = \left( \frac{1 + (-2)}{2}, \frac{2 + (-1)}{2} \right) = \left( \frac{-1}{2}, \frac{1}{2} \right) \]
2. Slope (m) of Line AB
The slope m of the line through points A and B is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates: \[ m = \frac{-1 - 2}{-2 - 1} = \frac{-3}{-3} = 1 \]
3. Distance (d) between A and B
The distance d between the points A and B is given by the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates: \[ d = \sqrt{((-2) - 1)^2 + ((-1) - 2)^2} = \sqrt{(-3)^2 + (-3)^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} \]
Please clarify if you meant A' and B' in a different context (e.g., reflection, rotation, etc.) for further assistance!