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).

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Solution

Midpoint of (5,7) and (3,9)
= $left parenthesis fraction numerator 5 plus 3 over denominator 2 end fraction comma fraction numerator 7 plus 9 over denominator 2 end fraction right parenthesis space equals space left parenthesis 4 comma 8 right parenthesis$

Midpoint of (8,6) and (0,10)
= $left parenthesis fraction numerator 8 plus 0 over denominator 2 end fraction comma fraction numerator 10 plus 6 over denominator 2 end fraction right parenthesis equals left parenthesis 4 comma 8 right parenthesis$

Hence the midpoint of both the lines are same.

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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).

Midpoint of (5,7) and (3,9) = Midpoint of (8,6) and (0,10) = Hence the midpoint of both the lines are same.