if line segment ru is considered the base of parallelogram rstu, what is the corresponding height of the…

Explanation:

Step1: Identify coordinates of the vertices

From the grid, the coordinates are $R(1, 1)$, $S(7, 0)$, $T(10, 4)$, and $U(4, 5)$.

Step2: Calculate the area of the parallelogram

Using the shoelace formula for vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3), (x_4, y_4)$: $$Area = |(x_R y_S + x_S y_T + x_T y_U + x_U y_R) - (y_R x_S + y_S x_T + y_T x_U + y_U x_R)|$$ $$Area = |(1 \cdot 0 + 7 \cdot 4 + 10 \cdot 5 + 4 \cdot 1) - (1 \cdot 7 + 0 \cdot 10 + 4 \cdot 4 + 5 \cdot 1)|$$ $$Area = |(0 + 28 + 50 + 4) - (7 + 0 + 16 + 5)| = |82 - 28| = 54$$

Step3: Calculate the length of base $RU$

Use the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ for $R(1, 1)$ and $U(4, 5)$: $$b = \sqrt{(4 - 1)^2 + (5 - 1)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$

Step4: Solve for the corresponding height

The area of a parallelogram is $Area = base \times height$. $$54 = 5 \times h$$ $$h = \frac{54}{5} = 10.8$$

Answer:

10.8 units