Question

Find x if distance between points L (2 ,-2, ) and M (-1, x) is 5​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

x = –6 or 2

Step-by-step explanation:

Apply Distance Formula:

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

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

Squaring on both sides

${5}^{2} = { - 3}^{2} + (x + 2)^{2}$

$25 = 9 + {x}^{2} + {2}^{2} + 2(x)(2)$

$25 - 9 - 4 = {x}^{2} + 4x \\ 25 - 13 = {x}^{2} + 4x \\ 12 = {x }^{2} + 4x$

Shift everything on one side

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

Do Factorisation

${x}^{2} + 6x - 2x - 12 = 0 \\ x(x + 6) - 2(x + 6) = 0 \\ (x + 6)(x - 2) = 0$

$x + 6 = 0 \: or \: x - 2 = 0 \\ x = - 6 \: or \: x = 2$