Pregunta
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EXEHCRCE 1 posints , B nt
  1. Calenier a pour que le linnghe Afri wit rockingte ewn 06
  2. Soit. le symetrigue de B par mopputt a M G. Geluler lea coordonnees de
  3. Quethe est In Hature du quandrlatóre ADCD? On justiflera la réponce sama effuct wer le moindre calcal
  4. Calculer l’aire du quarinilatere ot win perimetere (on donnera ce resist sout bis forme ef bentiers. b le plus petit. possible)
  5. a) Développer, réduire et ordonner .

Ask by Chan Little. in Togo
Jan 23,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

  • Coordinates of
  • Area of quadrilateral
  • Perimeter of quadrilateral
  • Expanded form of

Solución

Let’s break down the problem step by step.

1. Find such that the line is parallel to the line .

Known Points:
Step 1: Calculate the slope of line .
The slope is given by the formula:
Step 2: Calculate the slope of line .
The slope is given by:
Step 3: Set the slopes equal for parallel lines.
Since is parallel to :
Step 4: Cross-multiply and solve for .

2. Find the coordinates of point , the symmetric of with respect to point .

Step 1: Find the midpoint of segment .
The coordinates of are given by:
Step 2: Find the coordinates of point .
The coordinates of can be found using the midpoint formula:
Setting up the equations:
Solving for and :
  1. For :
  1. For :
Thus, .

3. Determine the nature of quadrilateral .

Step 1: Check if are vertices of a parallelogram.
To check if is a parallelogram, we can check if the midpoints of the diagonals and are the same.
Midpoint of :
Midpoint of :
Since the midpoints are not equal, is not a parallelogram.

4. Calculate the area of quadrilateral and its perimeter.

Step 1: Use the shoelace formula for area.
The area of quadrilateral can be calculated using the formula:
Substituting the coordinates:
Calculating the area:
Step 2: Calculate the perimeter.
The perimeter is the sum of the lengths of the sides:
Using the distance formula:

5. Develop, reduce, and order .

Step 1: Expand the expression.
Now, let’s calculate the area and perimeter of quadrilateral and provide the final results.

Final Calculations

I will now calculate the area and perimeter using the shoelace formula and distance formula.
Calculate the value by following steps:
  • step0: Calculate:
  • step1: Remove the parentheses:
  • step2: Multiply the numbers:
  • step3: Multiply the numbers:
  • step4: Calculate:

    Calculate or simplify the expression .
    Calculate the value by following steps:
  • step0: Calculate:
  • step1: Remove the parentheses:
  • step2: Multiply the numbers:
  • step3: Multiply the numbers:
  • step4: Multiply the numbers:
  • step5: Multiply the numbers:
  • step6: Calculate:
  • step7: Remove the parentheses:
  • step8: Multiply the numbers:
  • step9: Multiply the numbers:
  • step10: Multiply the numbers:
  • step11: Multiply the numbers:
  • step12: Calculate:
  • step13: Remove the parentheses:
  • step14: Add the numbers:

    Calculate or simplify the expression .
    Calculate the value by following steps:
  • step0: Calculate:
  • step1: Subtract the terms:
  • step2: Subtract the terms:
  • step3: Remove the parentheses:
  • step4: Remove the parentheses:
  • step5: Remove the parentheses:
  • step6: Add the numbers:
  • step7: Subtract the numbers:
  • step8: Add the numbers:
  • step9: Add the numbers:
  • step10: Subtract the numbers:
  • step11: Subtract the numbers:
  • step12: Add the numbers:
  • step13: Convert the expressions:
  • step14: Add the numbers:
  • step15: Simplify the root:
  • step16: Convert the expressions:
  • step17: Add the numbers:
  • step18: Simplify the root:
  • step19: Calculate:
  • step20: Calculate:
  • step21: Remove 0:
  • step22: Simplify the root:
  • step23: Remove 0:
  • step24: Reduce fractions to a common denominator:
  • step25: Transform the expression:
  • step26: Reorder the terms:
  • step27: Add the numbers:
  • step28: Reduce the fraction:

Summary of Calculations

  1. Finding :
    • We found such that line is parallel to line .
  2. Coordinates of Point :
    • The coordinates of point are .
  3. Nature of Quadrilateral :
    • The quadrilateral is not a parallelogram since the midpoints of the diagonals and are not equal.
  4. Area of Quadrilateral :
    • The area calculated using the shoelace formula is . This indicates that points are collinear.
  5. Perimeter of Quadrilateral :
    • The perimeter is calculated as .
  6. Expansion of :
    • The expanded form is .

Final Results

  • Coordinates of
  • Area of quadrilateral
  • Perimeter of quadrilateral
  • Expanded form of

Respondido por UpStudy AI y revisado por un tutor profesional

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Beyond the Answer

Pour que le segment soit de longueur 6, nous utiliserons la formule de la distance entre deux points :
Ici, avec et , on sait que doit égaler 6. En remplaçant les coordonnées et en résolvant l’équation, on peut trouver la valeur de à partir du point .
Pour le point , le symétrique de par rapport à (le point milieu entre et ), on pourra utiliser les coordonnées de et les coordonnées de pour trouver les coordonnées de . Cela signifie que l’on doit équilibrer les coordonnées des deux points de manière à ce que reste au centre.

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