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Mathematics

Find the co-ordinates of the mid-point of the line segment joining :

(i) A(5, 7) and B(-3, -1)

(ii) P(-5, -8) and Q(3, 4)

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Answer

(i) Let mid-point of the line segment joining AB be P(x,y).

By using mid-point formula,

(x, y) = (x1+x22,y1+y22)\Big(\dfrac{x1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get :

⇒(x,y)=(5+(−3)2,7+(−1)2)⇒(x,y)=(22,62)⇒(x,y)=(1,3).\Rightarrow (x, y) = \Big(\dfrac{5 + (-3)}{2}, \dfrac{7 + (-1)}{2}\Big) \\[1em] \Rightarrow (x, y) = \Big(\dfrac{2}{2}, \dfrac{6}{2}\Big) \\[1em] \Rightarrow (x, y) = (1, 3).

Hence, the coordinates of mid-point are (1, 3).

(ii) Let mid-point of the line segment joining PQ be B(x,y).

By using mid-point formula,

(x, y) = (x1+x22,y1+y22)\Big(\dfrac{x1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get :

⇒(x,y)=(−5+32,−8+42)⇒(x,y)=(−22,−42)⇒(x,y)=(−1,−2).\Rightarrow (x, y) = \Big(\dfrac{-5 + 3}{2}, \dfrac{-8 + 4}{2}\Big) \\[1em] \Rightarrow (x, y) = \Big(\dfrac{-2}{2}, \dfrac{-4}{2}\Big) \\[1em] \Rightarrow (x, y) = (-1, -2).

Hence, the coordinates of mid-point are (-1, -2).

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