Question

If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is 7 or -1 -7 or 1 -7 or -1 7 or 1 ​

Answer 1

answer is :- x= 7

Step-by-step explanation:

distance = 5 , ( x, -1) ( 3, 2)

d = \sqrt{ {(x2 - x1)}^{2} } + {(y2 - y1)}^{2}d=

(x2−x1)

2

+(y2−y1)

2

\begin{gathered}5 = \sqrt{ {(3 - x)}^{2} } + {(2 + 1)}^{2} \\ 25 = 9 + {x}^{2} - 6x + 9 \\ 7 = {x}^{2} - 6x \\ {x}^{2} - 6x - 7 = 0\end{gathered}

5=

(3−x)

2

+(2+1)

2

25=9+x

2

−6x+9

7=x

2

−6x

x

2

−6x−7=0

\begin{gathered} {x}^{2} - 7x + x - 7 = 0 \\ x(x - 7) + 1(x - 7) = 0 \\ (x - 7) = 0 \: \: \: \: (x + 1) = 0 \\ x = 7 \: \: \: \: x = - 1\end{gathered}

x

2

−7x+x−7=0

x(x−7)+1(x−7)=0

(x−7)=0(x+1)=0

x=7x=−1

negative answer is not considered

Therefore x=7