Question

find x and y such that p(x,y), (0,0) and (3,-4) are the vertices of an equilateral triangle​

Answer 1

Step-by-step explanation:

༒☬ᶜᴿᴬᶻᵞkíllє®™r☬༒मोहबत को जो निभाते हैं उनको मेरा सलाम है, और जो बीच रास्ते में छोड़ जाते हैं उनको, हुमारा ये पेघाम हैं, “वादा-ए-वफ़ा करो तो फिर खुद को फ़ना करो, वरना खुदा के लिए किसी की ज़िंदगी ना तबाह करो”

Answer 2

Therefore the value of x is 4.96 and y is 0.6.

Given:

The vertices of the equilateral triangle:

P( x,y ), Q( 0,0 ) and R( 3,-4 )

To Find:

The value of x and y make the vertices an equilateral triangle.

Solution:

The given question can be solved as shown below.

Given the vertices of the equilateral triangle,

⇒ P( x,y ), Q( 0,0 ) and R( 3,-4 )

In an equilateral triangle, the distance between all the vertices is the same.

⇒ PQ = QR = RP

If A( x₁, y₁ ) and B( x₂, y₂ )  are two points, then the distance between them is given by,

⇒ AB = √ [ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]

Similarly the distance between Q and R = QR = √ [ ( 3 - 0 )² + ( -4 - 0 )² ] = 5 units

So the distance between PQ = the distance between RP = 5 units

⇒ The distance between PQ = √ [ ( 0 - x )² + ( 0 - y )² ] = √ x² + y² = 5

⇒ x² + y² = 25     (i.)

⇒ The distance between RP = √ [ ( x - 3 )² + ( y + 4 )² ] = 5

⇒ ( x - 3 )² + ( y + 4 )² = 25

⇒ x² + 9 - 6x + y² + 8y + 16 = 25

⇒ (x² + y²) - 6x + 8y = 0

⇒ From equation-(i.), 25 - 6x + 8y = 0      (ii.)

On solving the equations-(i.) and (ii.),

We get, y= 0.6 and x = 4.96

Therefore the value of x is 4.96 and y is 0.6.

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