find the mid point of the line joining 2,3 and -2,1 hence show that the mid point and the two end points are collinear
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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.
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