Find the equation of the right bisector of the line segment joining the points A(1, 0) and B(2, 3).
Given, The line segment joining the points (1,0) and (2,3)
To Find: Find the equation of line
Formula used: The equation of line is (y – y1) = m(x – x1)
Explanation: Here, The right bisector PQ of AB at C and is perpendicular to AB
So, The slope of the line with two points is, m
The slope of the line AB
We know, The product of two slopes of the perpendicular line is always – 1
Therefore, (slope of AB) × (slope of PQ) = – 1
Since Slope of PQ
Now, The coordinate of the mid – points
The coordinates of point C are
The required equation of PQ is (y – y1) = m(x – x1)
6y – 9 = – 2x + 3
x + 3y = 6
Hence, The equation of line is x + 3y = 6