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Question
Find the positive value of m for which the distance between the points A(5, −3) and B(13, m) is 10 units.
Solution
It is given that distance between A(5, −3) and B(13, m) is 10 units.
⇒ `"AB" = sqrt((5-13)^2 +(-3-"m")^2)`
⇒ `10 = sqrt(64+9+6"m"+"m"^2)`
⇒ 100 = 73 + 6m +m2
⇒ m2 + 6m - 27 = 0
⇒ m2 +9m - 3m - 27 =0
⇒ m (m+9) - 3 (m-9)=0
⇒ (m-3) (m+9) =0
⇒ m=3, -9
Hence, the positive value of m is 3.
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