The equation of perpendicular bisector of the line segment joining the point (1,2) and (-2,0) is:

Explanation

Let `AB` is the line segment joining the point `(1,2) and (-2,0)`
and `C` is the midpoint og `AB`.

The, coordinates of `C` will be `(-1/2,1)`.

Slope of `AB, m_(AB) = (0-2)/(-2-1) = 2/3`

Now, let `CL` is the perpendicular bisector of `AB`. Then,

`m_(CL)**m_(AB) = -1` (Here, `m_(CL)` is slope of `CL`)

`m_(CL)**2/3 = -1=> m_(CL) = -3/2`

Now, we know the slope and coordinates of point C. So, the equation will be,

`y-1 = -3/2(x+1/2) = > 4y-4 = -6x -3`

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