Question

Indicate the equation of the given line in standard form.The line that is the perpendicular bisector of the segment whose endpoints are R(-1, 6) and S(5, 5)

Answer 1

Three steps are required:
1. Find the mid-point (M) of the segment using

Mid-point (M)of a segment between points \(R(x_1,y_1)\) and \(S(x_2,y_2)\)
\(\large M=(\frac{x_1+x_2)}{2},\frac{y_1+y_2}{2})\)

2. Find the slope of segment RS using

Slope (m) between two points \(R(x_1,y_1)\) and \(S(x_2,y_2)\)
\(\Large m=\frac{y_2-y_1)}{x_2-x_1}\)

3. find the perpendicular bisector, line L through M with slope m. Here's a guide:

\(\color{teal}{m} \)= slope
\((\color{blue}{x_0},\color{purple}{y_0})\) = given point M

Equation of line \(\boxed{\color{red}{L: y-\color{purple}{y_0} = \color{teal}{m} (x-\color{blue}{x_0})}}\)

Example:
Find equation of the line with slope 2.5 passing through the point (4,3)
\(\color{teal}{m} = \color{teal}{2.5}\)
\((\color{blue}{x_0},\color{purple}{y_0})=(\color{blue}{4},\color{purple}{3})\)
\(L: (y-\color{purple}{3}) = \color{teal}{2.5} (x-\color{blue}{4}) => y-\color{purple}{3}=\color{teal}{2.5}x-10 => y = 2.5x-7\)