4) The midpoint of \( A B \) is \( M(2,-2) \). If the coordinates of \( A \) are \( (1,-3) \) what are the coordinates of \( B \) ? 5) Point \( M \) is the midpoint of \( A B \). If the coordinates of \( A \) are \( (-6,3) \) and the coordinates of \( B \) are \( (-4,5) \), what are the coordinates of \( M \) ?

**4) Finding the coordinates of \( B \) when the midpoint \( M(2,-2) \) and endpoint \( A(1,-3) \) are given:** Let \( B = (x,y) \). Since \( M \) is the midpoint of \( AB \), we have: \[ \frac{1+x}{2}=2 \quad \text{and} \quad \frac{-3+y}{2}=-2 \] * For the \( x \)-coordinate: \[ \frac{1+x}{2}=2 \quad \Longrightarrow \quad 1+x=4 \quad \Longrightarrow \quad x=3 \] * For the \( y \)-coordinate: \[ \frac{-3+y}{2}=-2 \quad \Longrightarrow \quad -3+y=-4 \quad \Longrightarrow \quad y=-1 \] Thus, the coordinates of \( B \) are: \[ (3,-1) \] --- **5) Finding the midpoint \( M \) when the endpoints \( A(-6,3) \) and \( B(-4,5) \) are given:** The midpoint \(\ M\) is found using: \[ M = \left(\frac{x_A+x_B}{2}, \frac{y_A+y_B}{2}\right) \] Substitute the coordinates of \( A \) and \( B \): \[ M = \left(\frac{-6+(-4)}{2}, \frac{3+5}{2}\right) = \left(\frac{-10}{2}, \frac{8}{2}\right) \] Compute the values: \[ M = (-5,4) \] Thus, the midpoint \( M \) is at: \[ (-5,4) \]