Question

If the distance between the two points (x,-7) and (0,2) √97 unit, the value of x is​

Answer 1

Answer:

$\sf{The \ value \ of \ x \ is \ 4 \ or \ -4.}$

Given:

$\sf{The \ distance \ between \ the \ two \ points} \\ \sf{(x,-7) \ and \ (0-2) \ is \ \sqrt97}$

To find:

• The value of x.

Solution:

$\boxed{\sf{Distance \ between \ to \ point=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}}}$

$\sf{\therefore{\sqrt{(x-0)^{2}+(-7-2)^{2}}=\sqrt97}}$

$\sf{On \ squaring \ both \ sides, \ we \ get}$

$\sf{x^{2}+81=97}$

$\sf{\therefore{x^{2}=97-81}}$

$\sf{\therefore{x^{2}=16}}$

$\sf{On \ taking \ square \ root \ of \ both \ sides}$

$\boxed{\sf{x=\pm \ 4}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ x \ is \ 4 \ or \ -4.}}}$