Show that the line containing the points (a, b) and (b, a), a b, is perpendicular to the line y = x. Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.
We show that the lines are perpendicular to line and also we show that the midpoints lie on the line
We are given that a line contains a point
Therefore the slope is
Comparing the slope with standard equation, we get
And on multiplying both the slopes we get .
Hence the line containing point is perpendicular to line
And clearly this point lies on
We proved that the two lines are perpendicular and the midpoint of (a,b) (b,a) lie on the line
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