\( X Y Z W \) is a parallelogram with diagonals \( \overline{X Z} \) and \( \overline{Y W} \) that interse at point \( A \). If \( Y A=2 t \) and \( W A=3 t-4 \), find \( Y A \). a 8 b \( \quad 10 \) c \( \quad 30 \)

In a parallelogram, the diagonals bisect each other. This means that point \( A \), where the diagonals intersect, is the midpoint of both diagonals \( \overline{XZ} \) and \( \overline{YW} \). Given: - \( Y A = 2t \) - \( W A = 3t - 4 \) Since \( A \) is the midpoint, \( Y A = W A \). Therefore, we can set up the equation: \[ 2t = 3t - 4 \] Solving for \( t \): \[ 2t - 3t = -4 \\ -t = -4 \\ t = 4 \] Now, substitute \( t = 4 \) back into \( Y A \): \[ Y A = 2t = 2 \times 4 = 8 \] **Answer:** **a 8**