The distance between Point P ( 2 , 2 ) and Q ( 5, x ) is 5 cm then the

value of x =​

2 thoughts on “The distance between Point P ( 2 , 2 ) and Q ( 5, x ) is 5 cm then the <br /><br />value of x =​”

1. Answer:

   hope it helps

   Step-by-step explanation:

   use distance formula

   5=√(5-2)²+(x-2)²

   5=√(3)²+(x²+4+4x)

   5=√9+4+4x+x²

   5=√14+4x+x²

   squaring on both sides

   25= 14 + 4x + x²

   x²+4x-11=0

   solve the quadratic equation

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2. GiveN :-

   • The distance between Point P ( 2 , 2 ) and Q ( 5, x ) is 5 cm .

   To FinD :-

   • The value of x .

   SolutioN :-

   Given that the distance between two points , P(2,2) and Q (5,x) is 5 cm . We need to Find the value of x . We can use here distance formula which can be used ti Find the distance between two points (x1 , y1 ) and (x2 , y2) as ,

   [tex]\sf:\implies \pink{ Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}\\\\\sf:\implies 5cm = \sqrt{ (5-2)^2+(x-2)^2}\\\\\sf:\implies (5cm)^2 = (\sqrt{3^2+x^2+4-4x})^2 \\\\\sf:\implies 25cm^2 = 9 + x^2+4-4x \\\\\sf:\implies x^2+-4x +13 -25 = 0 \\\\\sf:\implies x^2-4x -12 =0 \\\\\sf:\implies x^2-6x +2x-12=0\\\\\sf:\implies x(x-6)+2(x-6) = 0 \\\\\sf:\implies(x-6)(x+2) =0\\\\\sf:\implies\underset{\blue{\sf Required \ Answers}}{\underbrace{\boxed{\pink{\frak{ x = 6 , -2}}}}} [/tex]

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