There are 5 black keys for each 7 white keys. Hence, the ratio stands at 5:7. To determine how many black keys correspond to 49 white keys, we calculate the scaling factor for the ratio: 49 divided by 7 equals 7. Thus, the original ratio is scaled by 7. Therefore, the total number of black keys equals 5 multiplied by this scaling factor, resulting in 35 black keys.
The characterization of HIJK as a parallelogram arises from the fact that the midpoints of both diagonals coincide at (1, 0), which indicates that these diagonals bisect each other. To explicitly demonstrate this, we determine that the midpoints of the diagonals HJ and IK are equal, confirming HIJK's properties as a parallelogram.
