# Find the values of y for which the distance between the points P(2, – 3) and Q (10, y) is 10 units.

Given: Distance between (2, - 3) and (10, y) is 10

To find: y

By distance formula, Distance between two points A(x1, y1) and B(x2, y2) is

AB = √((x2 - x1)2 + (y2 - y1)2)

Therefore,

√[(2 - 10)2 + (-3- y)2] = 10

√[(-8)2 + (3+ y)2] = 10

Squaring both sides to remove the square root,

⇒ 64 + (y + 3)2 = 100

⇒  (y + 3)2 = 100 - 64

⇒ (y + 3)2 = 36

⇒ y + 3 = ±6

⇒ (y + 3) will give two values 6 and -6 as answer because both the values when squared will give 36 as answer.)

y + 3 = 6 or y + 3 = -6

Therefore, y = 3 or -9

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