Question

if the distance between the point (x -1) and (3 ,2) is 5 then the value of x is​

Answer 1

Answer:

the value of x is 1 and -7

Answer 2

Given:

• Points are ( x , -1) and ( 3 , 2)

• distance = 5 .

To find :

• The value of x.

Solution :

• As we know that :

$\star \bold{ \red{ d \: = \sqrt{( {x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } }}$

Here ,

• x1 = x and y1 = -1

• x2 = 3 and y2 = 2

$\implies \: 5 = \sqrt{ {(3 - x)}^{2} + {(2 - ( - 1))}^{2} } \\ \\ \implies \: 25 = {(3 - x)}^{2} + {3}^{2} \\ \\ \implies \: 25 = 9 + {x}^{2} - 6x + 9 \\ \\ \implies \: {x}^{2} - 6x - 7 = 0 \\ \\ \implies \: {x}^{2} - 7x + x - \: 7 = 0 \\ \\ \implies \: x(x - 7) + 1(x - 7) = 0 \\ \\ \implies \: (x + 1)(x - 7) = 0 \\ \\ \implies \: x = - 1 \: \: and \: \: 7$

Hence , the value of x is 7.