a.) Find the coordinate of \( A \) if the midpoint of \( \overline{A B} \) is at \( (-1,-2) \) and \( B \) is at \( (3,-5) \). \( A \) is at: b.) Graph the rest of the line \( \overline{A B} \) and place a dot at point \( A \).

To find the coordinate of \( A \), you can use the midpoint formula, which states that the midpoint \( M \) of a segment connecting points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Here, we know the midpoint \( M(-1, -2) \) and point \( B(3, -5) \). Let the coordinates of \( A \) be \( (x_A, y_A) \). From the midpoint coordinates, we have: \[ \frac{x_A + 3}{2} = -1 \quad \text{and} \quad \frac{y_A - 5}{2} = -2 \] Solving for \( x_A \): \[ x_A + 3 = -2 \quad \Rightarrow \quad x_A = -2 - 3 = -5 \] Solving for \( y_A \): \[ y_A - 5 = -4 \quad \Rightarrow \quad y_A = -4 + 5 = 1 \] Thus, the coordinate of \( A \) is \( (-5, 1) \). To graph the line \( \overline{A B} \), plot the points \( A(-5, 1) \) and \( B(3, -5) \) on a Cartesian plane. Draw a straight line connecting them. You might want to mark each point clearly with a dot and label them. This way, you can visualize the distance and direction from \( A \) to \( B \) and appreciate the linear relationship between these two points!