Question

COORDINATE GEOMETRY
CLASS 10
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•Please answer the question in the picture.
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THANKS...​ ​​please answer please pleaseP​

Answer 1

Answer:

x=8 and y=4

Step-by-step explanation:

Let A(3,3) , B(6,Y) , C(X,7) and D(5,6)

AC and BD are the diagonals.

∴Coordinate of mid point of diagonal AC = (3+x)/2 , (7+3)/2

= (3+x)/2 , 10/2

Coordinates of mid point of diagonal BD = (5+6 )/2 , (6+y) /2

= 11/2 , (6+y)/2

Comparing the x coordinates of mid point of both diagonals,

(3+x)/2=11/2

3+x=11

∴ x=8

Comparing the y coordinates of midpoint of both diagonals,

(6+y)/2 = 10/2

6+y=10

∴y=4

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Answer 2

AnsWer :

• x = 8.
• y = 4.

QuestioN :

If ( 3 , 3 ) , ( 6 , y ) , ( x , 7 ) & ( 5 , 6 ) are the vertices of a parallelogram taken in order, find the value of ' x ' & ' y '.

To FinD :

find the value of ' x ' & ' y '.

SolutioN :

Let point be,

• A( 3 , 3 )
• B( 6 , y )
• C( x , 7 )
• D( 5 , 6 )
• Intersecting diagonal at a point be O.

Now,

By Mid-point Formula,

$\tt \bigstar \: \: \: \: \: \Bigg\lgroup \dfrac{ x_1 + x_2}{2} , \dfrac{y_1+y_2}{2}\Bigg\rgroup$

For Diagonal AC

$\tt \mapsto \: \: \: \: \: \Bigg\lgroup \dfrac{ 3 + x}{2} , \dfrac{3+7}{2}\Bigg\rgroup$

$\tt \mapsto \: \: \: \: \: \Bigg\lgroup \dfrac{ 3 + x}{2} , \dfrac{10}{2}\Bigg\rgroup$

$\tt \mapsto \: \: \: \: \: \Bigg\lgroup \dfrac{ 3 + x}{2} , 5\Bigg\rgroup$

Compare With AC( x' , y' )

• x' = 3 + x / 2.
• y' = 5.

$\rule{200}3$

For Diagonal BD

$\tt \mapsto \: \: \: \: \: \Bigg\lgroup \dfrac{ 6 + 5}{2} , \dfrac{y+6}{2}\Bigg\rgroup$

$\tt \mapsto \: \: \: \: \: \Bigg\lgroup \dfrac{11}{2} , \dfrac{y+6}{2}\Bigg\rgroup$

Compare With BD( x' , y' )

• x' = 11 / 2.
• y' = y + 6 / 2.

Now, we know that diagonal of AC and BD intersecting at a point O( let above )

$\tt \mapsto \: \: \: \: \: \dfrac{3 + x}{2} = \dfrac{11}{2}$

$\tt \mapsto \: \: \: \: \: 3 + x = 11.$

$\tt \mapsto \: \: \: \: \: x = 11 - 3.$

$\tt \mapsto \: \: \: \: \: x =8.$

$\rule{200}3$

$\tt \mapsto \: \: \: \: \: \dfrac{y + 6}{2} = 5.$

$\tt \mapsto \: \: \: \: \: y + 6 = 10$

$\tt \mapsto \: \: \: \: \:y = 10 - 6.$

$\tt \mapsto \: \: \: \: \:y = 4.$

• Coordinate O( 8 , 4 )

Therefore, the value of x is 8 and y is 4.

$\rule{200}3$

MorE Information :

• Section Formula.

$\tt \bigstar \: \: \: \: \: \Bigg\lgroup \dfrac{ m_1x_2 + m_2x_1}{m_1+m_2} , \dfrac{m_1y_2 + m_2y_1}{m_1+m_2} \Bigg\rgroup$

• Mid-point Formula.

$\tt \bigstar \: \: \: \: \: \Bigg\lgroup \dfrac{ x_1 + x_2}{2} , \dfrac{y_1+y_2}{2}\Bigg\rgroup$

• Distance Formula.

$\tt \bigstar \: \: \: \: \: D = \sqrt{(x_1+x_2)^2-(y_1+y_2)^2}$