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Question
Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).
Solution
We have two points A (5, 7) and B (3, 9) which form a line segment and similarly
C (8, 6) and D (0, 10) form another line segment.
We have to prove that mid-point of AB is also the mid-point of CD.
In general to find the mid-point P(x,y) of two points `A(x_1,y_1)` and `B(x_2, y_2)` we use section formula as,
`P(x,y) = ((x_1 + x_2)/2, (y_1 +y_2)/2)`
Therefore mid-point P of line segment AB can be written as,
`P(x,y) = ((5 + 3)/2, (7 + 9)/2)`
Now equate the individual terms to get,
x = 4
y = 8
So co-ordinates of P is (4, 8)
Similarly mid-point Q of side CD can be written as,
Q(x,y) = `((8 + 0)/2 "," (6 + 10)/2)`
Now equate the individual terms to get,
x= 4
y = 8
So co-ordinates of Q is (4, 8)
Hence the point P and Q coincides.
Thus mid-point of AB is also the mid-point of CD.
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