graph and label the quadrilateral with the given vertices. then determine the most precise name for the quadrilateral.

$p(-6, -3)$, $q(-2, 6)$, $r(2, 6)$, $s(6, -3)$

choose the correct graph of pqrs below.

Question

graph and label the quadrilateral with the given vertices. then determine the most precise name for the quadrilateral.

$p(-6, -3)$, $q(-2, 6)$, $r(2, 6)$, $s(6, -3)$

choose the correct graph of pqrs below.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Coordinate Geometry", "Classifying Quadrilaterals", "Isosceles Trapezoid Properties" ], "new_concepts": [], "current_concepts": [ "Coordinate Geometry", "Classifying Quadrilaterals", "Isosceles Trapezoid Properties" ] } ## Identify the correct graph of the vertices $$ \begin{aligned} P &= (-6, -3) \ Q &= (-2, 6) \ R &= (2, 6) \ S &= (6, -3) \end{aligned} $$ Comparing these coordinates to the options: - Option A shows a parallelogram. - Option B shows an isosceles trapezoid with vertices matching $P(-6, -3)$, $Q(-2, 6)$, $R(2, 6)$, and $S(6, -3)$. - Option C shows a rectangle. - Option D shows a trapezoid with incorrect coordinates. ## Calculate side lengths and slopes to classify the quadrilateral $$ \begin{aligned} \text{Slope of } QR &= \frac{6 - 6}{2 - (-2)} = 0 \ \text{Slope of } PS &= \frac{-3 - (-3)}{6 - (-6)} = 0 \ \text{Slope of } PQ &= \frac{6 - (-3)}{-2 - (-6)} = \frac{9}{4} = 2.25 \ \text{Slope of } RS &= \frac{-3 - 6}{6 - 2} = -\frac{9}{4} = -2.25 \ \text{Length of } PQ &= \sqrt{(-2 - (-6))^2 + (6 - (-3))^2} = \sqrt{4^2 + 9^2} = \sqrt{97} \ \text{Length of } RS &= \sqrt{(6 - 2)^2 + (-3 - 6)^2} = \sqrt{4^2 + (-9)^2} = \sqrt{97} \end{aligned} $$ ## Determine the most precise name $$ \begin{aligned} QR \parallel PS &\quad (\text{both slopes are } 0) \ PQ ot\parallel RS &\quad (\text{slopes are } 2.25 \text{ and } -2.25) \ PQ = RS = \sqrt{97} &\quad (\text{non-parallel legs are congruent}) \end{aligned} $$ Therefore, the quadrilateral is an isosceles trapezoid. ## Question 1 (A) Graph A

(B) Graph B

(C) Graph C

(D) Graph D ## Question 2 The most precise name for the quadrilateral is **isosceles trapezoid**. { "elements": [ { "type": "point", "params": [[-6, -3]], "properties": { "name": "P", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-2, 6]], "properties": { "name": "Q", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[2, 6]], "properties": { "name": "R", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[6, -3]], "properties": { "name": "S", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "polygon", "params": [[-6, -3], [-2, 6], [2, 6], [6, -3]], "properties": { "fillColor": "rgba(140, 85, 242, 0.2)", "strokeColor": "#8C55F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Classifying Quadrilaterals" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the correct graph of the vertices

Calculate side lengths and slopes to classify the quadrilateral

Determine the most precise name

Answer:

Question 1

Question 2