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in Coordinate Geometry by (49.2k points)
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Find the value of x if the distance between the points (2, –11) and (x, –3) is 10 units.

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Given, \(\sqrt{(x-2)^2+(-3-(-11))^2} = 10\)

⇒ \(\sqrt{(x-2)^2+64} = 10\)

⇒ \(\sqrt{x^2-4x+4+64}=10\)

⇒ x2 – 4x + 68 = 100 

⇒ x2 – 4x – 32 = 0 

⇒ (x – 8) (x + 4) = 0 

⇒ x = 8 or – 4

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