in parallelogram lmno, $mp = 21\text{ m}$, $lp = (y + 3)\text{ m}$, $np = (3y - 1)\text{ m}$, and $op = (2x - 1)\text{ m}$. what are the values of $x$ and $y$?

$x = 10\text{ m}, y = 1\text{ m}$
$x = 10\text{ m}, y = 2\text{ m}$
$x = 11\text{ m}, y = 1\text{ m}$
$x = 11\text{ m}, y = 2\text{ m}$

Question

in parallelogram lmno, $mp = 21\text{ m}$, $lp = (y + 3)\text{ m}$, $np = (3y - 1)\text{ m}$, and $op = (2x - 1)\text{ m}$. what are the values of $x$ and $y$?

$x = 10\text{ m}, y = 1\text{ m}$
$x = 10\text{ m}, y = 2\text{ m}$
$x = 11\text{ m}, y = 1\text{ m}$
$x = 11\text{ m}, y = 2\text{ m}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallelogram Diagonals Theorem" ], "new_concepts": [], "current_concepts": [ "Parallelogram Diagonals Theorem" ] } ## Set up equations using the Parallelogram Diagonals Theorem $$ \begin{aligned} &LP = NP \implies y + 3 = 3y - 1 \ &MP = OP \implies 21 = 2x - 1 \end{aligned} $$ ## Solve for y $$ \begin{aligned} &y + 3 = 3y - 1 \ &2y = 4 \ &y = 2\text{ m} \end{aligned} $$ ## Solve for x $$ \begin{aligned} &2x - 1 = 21 \ &2x = 22 \ &x = 11\text{ m} \end{aligned} $$

$x = 10\text{ m}, y = 1\text{ m}$

$x = 10\text{ m}, y = 2\text{ m}$

$x = 11\text{ m}, y = 1\text{ m}$

$x = 11\text{ m}, y = 2\text{ m}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallelogram Diagonals Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up equations using the Parallelogram Diagonals Theorem

Solve for y

Solve for x

Answer: