Question

Find x if distance between points L(x, 7) and M(1, 15) is 10.
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Answer 1

Answer:

this will be the ANSWER.

Answer 2

✰ Question :-

• Find x if distance between points L(x ,7) and M(1,15) is 10.

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✰ Solution :-

• Distance between LM = 10 (given)

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Formula to be used :-

$\large {\boxed {\frak {\underline{\red { Distance \; Formula \; = \sqrt { ( x_2 - x_1 )^2 + ( y_2 - y_1 )^2 } }}}}}$

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ㅤ‎‎‎‎ㅤ$\small {\frak {\underline {\purple { Substituting \; the \; values \; in \; Formula :-}}}}$

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$\implies {\sf { 10 = \sqrt { ( 1 - x )^2 + ( 15 - 7 ) ^2 }}}$

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Using identity :- (a-b) ² = a² + b² - 2ab

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$\implies {\sf { 10 = \sqrt { 1 + x^2 -2x + (8)^2 }}}$

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$\implies {\sf { 10^2 = x^2 - 2x + 65}}$

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$\implies \sf {100 = x^2 - 2x + 65}$

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$\implies \sf {0 = x^2 - 2x + 65 - 100}$

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$\implies \sf {0 = x^2 - 2x -35}$

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Now, factorising :-

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$\implies \sf { x^2 - 7x +5x - 35= 0}$

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$\implies \sf { x(x-7) + 5(x-7)}$

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$\implies \sf { (x-7)(x+5)}$

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$\implies \sf { x = -5 , 7}$

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Therefore, x = -5 or 7 .