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

4.5 units
5.4 units
9.0 units
10.8 units

Question

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

4.5 units
5.4 units
9.0 units
10.8 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Shoelace Formula", "Area of Polygons" ], "new_concepts": [ "Parallelogram Height in Coordinate Plane" ], "current_concepts": [ "Shoelace Formula", "Area of Polygons", "Parallelogram Height in Coordinate Plane" ] } ## Identify the coordinates of the vertices Find the coordinates of the vertices of parallelogram $RSTU$ from the grid: - $R = (1, 1)$ - $S = (7, 0)$ - $T = (10, 4)$ - $U = (4, 5)$ ## Calculate the area of the parallelogram Using the *Shoelace Formula* knowledge point $$ \begin{aligned} \text{Area} &= \frac{1}{2} |(1\cdot0 + 7\cdot4 + 10\cdot5 + 4\cdot1) - (1\cdot7 + 0\cdot10 + 4\cdot4 + 5\cdot1)| \ &= \frac{1}{2} |(0 + 28 + 50 + 4) - (7 + 0 + 16 + 5)| \ &= \frac{1}{2} |82 - 28| \ &= \frac{1}{2} \cdot 54 \ &= 27 \end{aligned} $$ ## Calculate the length of the base RU Using the *Area of Polygons* knowledge point $$ \begin{aligned} RU &= \sqrt{(4 - 1)^2 + (5 - 1)^2} \ &= \sqrt{3^2 + 4^2} \ &= \sqrt{9 + 16} \ &= 5 \end{aligned} $$ ## Calculate the corresponding height Using the *Area of Polygons* knowledge point $$ \begin{aligned} \text{Area} &= \text{base} \times \text{height} \ 27 &= 5 \times h \ h &= \frac{27}{5} \ h &= 5.4 \end{aligned} $$

(A) 4.5 units

(B) 5.4 units

(C) 9.0 units

(D) 10.8 units

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QUESTION IMAGE

Question

Explanation:

Identify the coordinates of the vertices

Calculate the area of the parallelogram

Calculate the length of the base RU

Calculate the corresponding height

Answer: