Question

if The distance between two
Points (x,7) & ( 1,15) is
10 find a value x
​

Answer 1

Answer:

${\large{\sf{\underline{Given}}}}$

$\: \: \: \: \: \: \: \: { \sf{❍ \: Distance \: Between \: Points \: (1,15) \: and \: (x, 7) \: is \: 10}}$

${\large{\sf{\underline{To \: Find}}}}$

$\: \: \: \: \: \: \: \: { \sf{❍ \: Value \: of \: x???}}$

${\large{\sf{\underline{Solution}}}}$

• By using distance formula, we can get value of x. let's start our solution.

${\underline{ \sf{★ \: Formula\: used,}}}$

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

${\underline{ \sf{★ \: By\: Solving,}}}$

${\dashrightarrow{\sf{ \sqrt{ {(x - 1)}^{2} + {(7 - 15)}^{2} } = 10}}} \\ \\ \\ { \sf{Squaring \: on \: both \: sides}} \\ \\ \\ {\dashrightarrow{\sf{( {x - 1)}^{2} + {8}^{2} = 100 }}} \\ \\ \\ {\dashrightarrow{\sf{ {x}^{2} + 1 - 2x + 64 = 100}}} \\ \\ \\ {\dashrightarrow{\sf{ {x}^{2} - 2x +65 = 100 }}} \\ \\ \\ {\dashrightarrow{\sf{ {x}^{2} - 2x = 100 - 65}}} \\ \\ \\ {\dashrightarrow{\sf{ {x}^{2} - 2x = 35 }}} \\ \\ \\ {\dashrightarrow{\sf{ {x}^{2} - 2x - 35 = 0}}} \\ \\ \\ {\dashrightarrow{\sf{ {x}^{2} - 7x + 5x - 35 = 0 }}} \\ \\ \\ {\dashrightarrow{\sf{x(x - 7) + 5(x - 7) = 0}}} \\ \\ \\ {\dashrightarrow{\sf{(x + 5)(x - 7) = 0}}} \\ \\ \\ {\dashrightarrow{\sf{x = - 5 \: or \: 7}}} \\ \\ \\ { \boxed{ \boxed{ \therefore{ \sf{ \pink{Value \: of \: x \: is \: 7}}}}}}$