Find the equation of the right bisector of the line segment joining th

1.	Find the equation of the right bisector of the line segment joining the points A(1, 0) and B(2, 3).
Answer» 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 = \(\frac{y_2-y_1}{x_2-x_1}\) The slope of the line AB = \(\frac{3-0}{2-1}\) = 3 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 = \(-\frac{1}{3}\) Now, The coordinate of the mid – points = \([\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}]\) The coordinates of point C are = \([\frac{1+2}{2},\frac{3+0}{2}]\) = \([\frac{3}{2}, \frac{3}{2}]\) The required equation of PQ is (y – y₁) = m(x – x₁) \(\Big(y-\frac{3}{2}\Big)\) = \(-\frac{1}{3}\Big(x-\frac{3}{2}\Big)\) 6y – 9 = – 2x + 3 x + 3y = 6 Hence, The equation of line is x + 3y = 6

Find the equation of the right bisector of the line segment joining the points A(1, 0) and B(2, 3).

Answer»

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 = \(\frac{y_2-y_1}{x_2-x_1}\)

The slope of the line AB = \(\frac{3-0}{2-1}\) = 3

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 = \(-\frac{1}{3}\)

Now, The coordinate of the mid – points = \([\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}]\)

The coordinates of point C are = \([\frac{1+2}{2},\frac{3+0}{2}]\) = \([\frac{3}{2}, \frac{3}{2}]\)

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

\(\Big(y-\frac{3}{2}\Big)\) = \(-\frac{1}{3}\Big(x-\frac{3}{2}\Big)\)

6y – 9 = – 2x + 3

x + 3y = 6

Hence, The equation of line is x + 3y = 6