Math, asked by khalidk2956, 9 months ago

Find the value of y for which the distance between the point P(4,-6) and Q(20,y) is 20 units

Answers

Answered by BrainlyPopularman
10

GIVEN :

• Points are P(4,-6) and Q(20,y).

• Distance between them is 20 unit.

TO FIND :

• Value of 'y' = ?

SOLUTION :

• We know that Distance between two points is –

  \\ \large \implies { \boxed{\bf Distance =  \sqrt{(x_{2} - x_{1}) ^{2} +  {(y_{2} - y_{1})}^{2} }}} \\

• Here –

  \\ \bf  \implies x_{1} = 4\\

  \\ \bf  \implies x_{2} =20 \\

  \\ \bf  \implies y_{1} = -6\\

  \\ \bf  \implies y_{2} =y\\

• Now put the values –

  \\ \implies\bf Distance =  \sqrt{(20-4) ^{2} +  {(y-( - 6))}^{2} }  \\

  \\ \implies\bf 20 =  \sqrt{(16) ^{2} +  {(y + 6)}^{2} }  \\

• Square on both sides –

  \\ \implies\bf (20)^{2} = (16)^{2} +  {(y + 6)}^{2}\\

  \\ \implies\bf {(y + 6)}^{2} =(20)^{2} - (16) ^{2} \\

  \\ \implies\bf {(y + 6)}^{2} =(20- 16)(20 + 16) \\

  \\ \implies\bf {(y + 6)}^{2} =(4)(36) \\

  \\ \implies\bf {(y + 6)}^{2} =144 \\

  \\ \implies\bf y + 6 = \sqrt{144} \\

  \\ \implies\bf y + 6 = \pm 12\\

  \\ \implies\bf y =  - 6\pm 12\\

  \\ \implies\bf y =  - 6 + 12, - 6 - 12\\

  \\ \implies \large{ \boxed{\bf y = 6,-18}}\\

Hence , The value of 'y' is 6 'or' -18.

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