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Mathematics

The mid-point of the line segment joining the points (1, -6), (3, x) is (2, 6). The value of x is :

  1. 1

  2. 2

  3. 18

  4. -18

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,

The mid-point of the line segment joining the points (1, -6), (3, x) is (2, 6).

∴(2,6)=(1+32,−6+x2)⇒(2,6)=(42,−6+x2)⇒(2,6)=(2,−6+x2)⇒6=−6+x2⇒12=−6+x⇒x=12+6=18.\therefore (2, 6) = \Big(\dfrac{1 + 3}{2}, \dfrac{-6 + x}{2}\Big) \\[1em] \Rightarrow (2, 6) = \Big(\dfrac{4}{2}, \dfrac{-6 + x}{2}\Big) \\[1em] \Rightarrow (2, 6) = \Big(2, \dfrac{-6 + x}{2}\Big) \\[1em] \Rightarrow 6 = \dfrac{-6 + x}{2} \\[1em] \Rightarrow 12 = -6 + x \\[1em] \Rightarrow x = 12 + 6 = 18.

Hence, Option 3 is the correct option.

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