Question

if the distance between two point (2,-2)and(-1,x) is 5 find x

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Answer 1

Answer:

2 or -6

Step-by-step explanation:

Formula for distance between two points

(x1,y1) ,(x2,y2) is

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

So, here

d = 5

x1 = 2, y1 = -2

x2 = -1, y2 = x

$5 = \sqrt{ {( - 1 - 2)}^{2} + {(y2 + 2)}^{2} }$

$25 = {( - 3)}^{2} + {y2}^{2} + 4 + 2 \times y2 \times 2$

${y2}^{2} + 9 - 25 + 4 + 4y2 = 0$

${y2}^{2} + 4y2 - 12 = 0$

${y2}^{2} + 6y2 - 2y2 - 12 = 0$

$y2(y2 + 6) - 2(y2 + 6) = 0$

$(y2 - 2)(y2 + 6) = 0$

$y2 = 2 \: and \: y2 = - 6$

The value of x will be 2 or -6