Question

Find all possible values of x for which the distance between the points A ( X , - 1) and B ( 5 , 3) is 5 units

Answer 1

$\textbf{Given:}$

$\text{Distance between A(x,-1) and B(5,3) is 5 units}$

$\textbf{To find:}$

$\text{The values of x}$

$\textbf{Solution:}$

$\text{Since distance between A(x,-1) and B(5,3) is 5 units, we have}$

$AB=5$

$\sqrt{(x_1-x_2)^2+(y_1-y_1)^2}=5$

$\sqrt{(x-5)^2+(-1-3)^2}=5$

$\sqrt{(x-5)^2+(-4)^2}=5$

$\sqrt{(x-5)^2+16}=5$

$\text{Squaring on bothsides, we get}$

$(x-5)^2+16=25$

$(x-5)^2=25-16$

$(x-5)^2=9$

$\text{Taking square root on bothsides, we get}$

$x-5=\pm{3}$

$x=5\pm{3}$

$\implies\;x=5+3\;\text{(or)}\;x=5-3$

$\implies\;x=8\;\text{(or)}\;x=2$

$\textbf{Answer:}$

$\textbf{The values of x are 8 and 2}$

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