A(3;9) B(10;5)
It looks like you have two points given: A(3, 9) and B(10, 5). If you need assistance with these points, here are a few things you might want to find:
Distance between points A and B: You can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the coordinates: \[ d = \sqrt{(10 - 3)^2 + (5 - 9)^2} = \sqrt{(7)^2 + (-4)^2} = \sqrt{49 + 16} = \sqrt{65} \approx 8.06 \]
Slope of the line segment AB: The slope (m) can be calculated using: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates: \[ m = \frac{5 - 9}{10 - 3} = \frac{-4}{7} \approx -0.571 \]
Equation of the line passing through A and B: Using the point-slope form of the equation of a line, which is \(y - y_1 = m(x - x_1)\):
- Substitute one of the points (let’s use A): \[ y - 9 = -\frac{4}{7}(x - 3) \] Reorganizing gives you: \[ y = -\frac{4}{7}x + \frac{12}{7} + 9 \] Standardizing this would give: \[ y = -\frac{4}{7}x + \frac{69}{7} \]
Midpoint of AB: The midpoint (M) can be calculated by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substituting the coordinates: \[ M = \left( \frac{3 + 10}{2}, \frac{9 + 5}{2} \right) = \left( \frac{13}{2}, 7 \right) = (6.5, 7) \]
If you need any specific calculations or further information about these points, let me know!
