Pregunta
EXEHCRCE 1 posints
, B
nt
- Calenier a pour que le linnghe Afri wit rockingte ewn 06
- Soit.
le symetrigue de B par mopputt a M G. Geluler lea coordonnees de
- Quethe est In Hature du quandrlatóre ADCD? On justiflera la réponce sama effuct wer le moindre calcal
- Calculer l’aire du quarinilatere
ot win perimetere (on donnera ce resist sout bis forme
ef bentiers. b le plus petit. possible)
- 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:
The slope
Step 2: Calculate the slope of line
.
The slope is given by:
The slope
Step 3: Set the slopes equal for parallel lines.
Since is parallel to
:
Since
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:
The coordinates of
Step 2: Find the coordinates of point
.
The coordinates of can be found using the midpoint formula:
The coordinates of
Setting up the equations:
Solving for
and
:
- For
:
- 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.
To check if
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:
The area
Substituting the coordinates:
Calculating the area:
Step 2: Calculate the perimeter.
The perimeter is the sum of the lengths of the sides:
The perimeter
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:
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
-
Finding
: - We found
such that line is parallel to line .
- We found
-
Coordinates of Point
: - The coordinates of point
are .
- The coordinates of point
-
Nature of Quadrilateral
: - The quadrilateral
is not a parallelogram since the midpoints of the diagonals and are not equal.
- The quadrilateral
-
Area of Quadrilateral
: - The area calculated using the shoelace formula is
. This indicates that points are collinear.
- The area calculated using the shoelace formula is
-
Perimeter of Quadrilateral
: - The perimeter is calculated as
.
- The perimeter is calculated as
-
Expansion of
: - The expanded form is
.
- 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
Como
error msg


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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