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in Coordinate Geometry by (49.2k points)
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If y is a positive integer such that the distance between the points (–6, –1) and (–6, y) is 12 units, then y = 

(a) 5 

(b) 8 

(c) 11 

(d) 1

1 Answer

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Best answer

(c) 11

Given, \(\sqrt{(-6+6)^2+(y+1)^2}\) = 12

⇒ \(\sqrt{y^2+2y+1}\) = 12

⇒ y2 + 2y + 1 = 144 ⇒ y2 + 2y – 143 = 0 

⇒ y2 + 13y – 11y – 143 = 0 

⇒ y (y + 13) – 11 (y + 13) = 0 

⇒ (y – 11) (y + 13) = 0 ⇒ y = 11 or –13 

The required positive integer is 11.

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