Given that line segment RU with vertices R(1, 1) and U(4, 5) is considered the base of parallelogram RSTU.
Then, the line segment ST with vertices S(7, 0) and T(10, 4) is the top of the parallelogram.
The corresponding height of the parallelogram is the length of a line with endponts at RU and ST and perpendicular to both RU and ST.
The equation of the line segment RU is given by

Recall that given that two lines are perpendicular, the product of the slope of the two lines is -1.
Let the slope of the line perpendicular to line RU be m, then

Thus, the equation of the line perpendicular to RU passing through point (1, 1) is given by

The equation of the line segment ST is given by

The line perpendicular to line segment RU intersected line segment ST at the point given by

Thus, the corresponding height of the parallelogram is the line with endpoints

Recall that the length of a line passing through points

is given by

Thus, the length of the line passing through points

is given by

Therefore, <span>the corresponding height of the given parallelogram is
5.4 units</span>