Q8 of 66 Page 7

Find the value of y for which the distance between the points A(3,-1) and B(11,y) is 10 units.(CBSE 2011)

Given: Distance between A and B = 10 units.

If A(x1, y1) and B(x2, y2) be two points, then the distance between points is given by:

(AB)2 = (x2 - x1)2 + (y2 - y1)2

(10)2 = (11 - 3)2 + (y – (-1))2

100 = (8)2 + (y + 1)2

100 = 64 + (y + 1)2

36 = (y + 1)2

Taking square root on both sides

(y + 1) = ± 6

y = ± 6 -1

Therefore y = 6 – 1 or y = - 6 -1

⇒ y = 5 or y = - 7

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