Q13 of 84 Page 114

If the length of the line segment with end points (2, −6) and (2, y) is 4, find y.

Formula used:


Given: Distance = 4 and coordinates of two points is A (2, –6) and B (2, y)


AB = √ (x2 – x1)2 + (y2 – y1)2


⇒ 4 = √ (2 – 2)2 + (y – (–6))2


⇒ 4 = √ (0) + (y + 6)2


Squaring both sides


⇒ 42 = (y + 6)2


⇒ 16 = y2 + 12y + 36


⇒ y2 + 12y + 36 – 16 = 0


⇒ y2 + 12y + 20 = 0


⇒ y2 + 10y + 2y + 20 = 0


⇒ y (y + 10) + 2(y + 10) = 0


⇒ (y + 2) (y + 10) = 0


y + 2 = 0 or y + 10 = 0


y = –2 or y = –10


∴ y = –2 or –10


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