First find the equation of the line, Ill use the first one as an example:
(-5,10) , ( -9,2)
To work out the gradient:
[tex] \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex] \frac{2 - 10}{-9 - -5} = \frac{-8}{-4} = 2 [/tex]
So the gradient of the line is 2
The midpoint of the line is [tex]( \frac{-5 + -9}{2}, \frac{10+2}{2}) = ( -3.5, 6) [/tex]
The gradient of the inverted line is -0.5 as it is the negative reciprocal of the gradient of the first line.
Here, we work out the equation of the bisector.
[tex]y-6 = -0.5(x+3.5) [/tex]
[tex]y-6 = \frac{-x}{2}-1.75 [/tex]
[tex]y = -\frac{1}{2} x+4.25[/tex]
