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Mathematics

P(m, m - 2) is the mid-point of the line segment AB, where A = (4, 6) and B = (-4, -10), then the value of m is :

  1. 0

  2. -2

  3. 2

  4. 4

Section Formula

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Answer

By formula,

Mid-point = (x1+x22,y1+y22)\Big(\dfrac{x1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Given, P is the mid-point of AB.

∴(m,m−2)=(4+(−4)2,6+(−10)2)⇒(m,m−2)=(02,−42)⇒(m,m−2)=(0,−2).∴m=0.\therefore (m, m - 2) = \Big(\dfrac{4 + (-4)}{2}, \dfrac{6 + (-10)}{2}\Big) \\[1em] \Rightarrow (m, m - 2) = \Big(\dfrac{0}{2}, \dfrac{-4}{2}\Big) \\[1em] \Rightarrow (m, m - 2) = (0, -2). \\[1em] \therefore m = 0.

Hence, Option 1 is the correct option.

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