Question

find the mid point of the line joining (2,3)and (-2,1) hence show that the midpoint and two points are collinear​

Answer 1

Required mid-point is (0, 2)

Step-by-step explanation:

The given points are (2, 3) and (- 2, 1)

Then the coordinates of the mid-point of the line joining these points are

( (2 - 2)/2, (3 + 1)/2 ), i.e., (0, 2)

The equation of the line passing through the points (2, 3) and (- 2, 1) is

(y - 3)/(3 - 1) = (x - 2)/(2 + 2)

or, (y - 3)/2 = (x - 2)/4

or, 2 (y - 3) = x - 2

or, 2y - 6 = x - 2

or, x - 2y + 4 = 0 ..... (1)

Putting x = 0 and y = 2 in the LHS of (1), we get

0 - 2 (2) + 4 = 0, equalling with the RHS of (1)

Thus (0, 2) lies on (1) no. line.

This proves the required collinearity.