Question

Find the positive value of m for which the distance between the points A(5, −3) and B(13, m) is 10 units.

Answer 1

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.