Respuesta :
Answer:
The equation of the perpendicular line is y = −4(x) − 6
Step-by-step explanation:
Given:
Three coordinates points (in pair).
Lets choose two points,in [tex](x,y)[/tex] format.
Where
[tex](x,y)[/tex] = [tex](-5,-3)[/tex] and [tex](x_1,y_1)[/tex] = [tex](3,-1)[/tex]
From these points we will find the slope using point-slope formula.
That is :
[tex](y_1-y)=m(x_1-x)[/tex]
[tex]m=\frac{(y_1-y)}{(x_1-x)}[/tex]
Plugging the values:
[tex]m=\frac{-1+3}{3+5}=\frac{1}{4}[/tex]
Now we know that product of slope of two perpendicular lines = -1.
So the slope of the line which is perpendicular [tex](m_1)[/tex] .
[tex]m_1=\frac{-1}{m}[/tex]
[tex]m_1=\frac{-1}{\frac{1}{4} } =-1\times \frac{4}{1} =-4[/tex]
Now using this slope we will plug the midpoint (-1,-2) values in point-slope form and reduced it to slope intercept.
[tex]y-(-2)=-4(x+1)[/tex]
[tex]y+2=-4x-4[/tex]
[tex]y=-4x-4-2[/tex]
[tex]y=-4x-6[/tex]
So the equation of the perpendicular bisector is y = -4(x) - 6
Answer:
y = -4(x) - 6
Step-by-step explanation:
For anyone looking for a simple answer.
