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).

Question

Philoid · Accepted Answer

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 = , y =

For midpoint of AB,

x = , y =

x = 4 and y = 8 …(1)

Now for midpoint of CD,

e = , d = …(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.