Questions: Plot the points A(3,-2), B(-3,8), C(-5,-1) on the coordinate axes below. State the coordinates of point D such that A, B, C, and D would form a parallelogram. (Plotting point D is optional.)

Solution Steps

Point A is at coordinates (3, -2). Point B is at coordinates (-3, 8). Point C is at coordinates (-5, -1).

To form a parallelogram, the midpoint of AC must be the same as the midpoint of BD. Midpoint of AC: $(\frac{3 + (-5)}{2}, \frac{-2 + (-1)}{2}) = (-1, -\frac{3}{2})$ Let D be $(x, y)$. Then the midpoint of BD is $(\frac{-3 + x}{2}, \frac{8 + y}{2})$. Equating the midpoints, we get: $\frac{-3 + x}{2} = -1$ => $-3 + x = -2$ => $x = 1$ $\frac{8 + y}{2} = -\frac{3}{2}$ => $8 + y = -3$ => $y = -11$ So, the coordinates of D are $(1, -11)$.

Final Answer