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).

Answer 1

Let given points be A(5, 7) and B(3, 9) and the points of other segment line be C(8, 6) and D(0, 10)

By midpoint formula.

x = \(\frac{x_1+x_2}2\), y = \(\frac{y_1+y_2}2\)

For midpoint of AB,

 x = \(\frac{5+3}2\), y = \(\frac{7+9}2\)

x = 4 and y = 8 …(1) 

Now for midpoint of CD,

e = \(\frac{a+0}2\), d = \(\frac{6+16}2\) …(say)

∴ e = 4 and d = 8 …(2) 

Here from 1 and 2 we say that midpoints of AB and CD are same, ie they coincide.