Question: Find the midpoint M of the line segment joining the points S = (-7, -5) and T = (1, 3).

Find the midpoint M of the line segment joining the points S = (-7, -5) and T = (1, 3).

Solution

To find the midpoint \( M \) of the line segment joining points \( S = (-7, -5) \) and \( T = (1, 3) \), use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substitute the given coordinates into the formula: 1. Assign the coordinates: - \( x_1 = -7 \), \( y_1 = -5 \) - \( x_2 = 1 \), \( y_2 = 3 \) 2. Calculate the \( x \)-coordinate of the midpoint: \[ \frac{-7 + 1}{2} = \frac{-6}{2} = -3 \] 3. Calculate the \( y \)-coordinate of the midpoint: \[ \frac{-5 + 3}{2} = \frac{-2}{2} = -1 \] 4. Write the coordinates of the midpoint: \[ M = (-3, -1) \]