Question

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

a) -7 or -1 b) -7 or 1 c) 7 or 1 d) 7 or -1​

Answer 1

Answer:

Ans: x=7

Step-by-step explanation:

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

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

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

${x}^{2} - 7x + x - 7 = 0 \\ x(x - 7) + 1(x - 7) = 0 \\ (x - 7) = 0 \: \: \: \: (x + 1) = 0 \\ x = 7 \: \: \: \: x = - 1$

negative answer is not considered

Therefore x=7

Answer 2

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