Find the equation

Given, The line segment joining the points (3,4) and ( – 1,2)

To Find: Find the equation of the 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

Now, The coordinate of the mid – points =

The coordinates of point C are = = (1,3)

And, The slope of PQ =

The slope of PQ, m =

SO, The slope of PQ, m = – 2

The required equation of PQ is (y – y₁) = m(x – x₁)

y – 3 = – 2(x – 1)

y – 3 = – 2x + 2

y + 2x = 5

Hence, The equation of line is y + 2x = 5