To find the midpoint of the line segment joining two points \( P(-3, 5) \) and \( Q(5, -3) \), we can use the midpoint formula. The midpoint \( M \) of a line segment connecting two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] ### Step-by-Step Calculation 1. **Identify the coordinates of the points**: - Point \( P \) has coordinates \( (x_1, y_1) = (-3, 5) \) - Point \( Q \) has coordinates \( (x_2, y_2) = (5, -3) \) 2. **Substitute the coordinates into the midpoint formula**: - For the x-coordinate of the midpoint: \[ x_M = \frac{x_1 + x_2}{2} = \frac{-3 + 5}{2} \] \[ x_M = \frac{2}{2} = 1 \] - For the y-coordinate of the midpoint: \[ y_M = \frac{y_1 + y_2}{2} = \frac{5 + (-3)}{2} \] \[ y_M = \frac{5 - 3}{2} = \frac{2}{2} = 1 \] 3. **Combine the results**: - The coordinates of the midpoint \( M \) are \( (1, 1) \). ### Conclusion Thus, the midpoint of the line segment joining points \( P(-3, 5) \) and \( Q(5, -3) \) is \( (1, 1) \). ### Explanation of Options - **Option A: (1, 1)** - This is the correct answer as we calculated the midpoint accurately. - **Option B: (2, 2)** - This option is incorrect. It does not match our calculated midpoint. - **Option C: (4, 4)** - This option is also incorrect. The coordinates do not correspond to the midpoint derived from the given points. - **Option D: (4, -4)** - This option is incorrect as well. The coordinates do not reflect the midpoint calculation. ### Common Pitfalls - **Miscalculating the sum of coordinates**: Ensure you add the x-coordinates and y-coordinates correctly. - **Forgetting to divide by 2**: The midpoint formula requires averaging the coordinates, which means dividing by 2. - **Confusing the order of points**: The order of points does not affect the midpoint, but it’s essential to keep track of which coordinates belong to which point. ### Revision Summary - The midpoint formula is \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \). - To find the midpoint, add the x-coordinates and y-coordinates separately, then divide each sum by 2. - The correct midpoint for points \( P(-3, 5) \) and \( Q(5, -3) \) is \( (1, 1) \). - Always double-check your calculations to avoid common mistakes.