Question

what is the equation, in slope-intercept form, of the perpendicular nose core of the given line segment?

Answer 1

Answer: Provided the three coordinate points, we have to find the equation of the perpendicular bisector of the provided line in slope intercept form:

`\begin{gathered} y(x)=mx+b \\ \\ m=(\Delta y)/(\Delta x) \end{gathered}`
`(-5,-3)\text{ }(-1,-2)\text{ }(3,-1)`

Equation of the line and the perpendicular bisector:

`\begin{gathered} m=(\Delta y)/(\Delta x)=(-2-(-1))/(-1-3)=(-1)/(-4)=(1)/(4) \\ \\ m=(1)/(4) \\ \\ \therefore\rightarrow \\ \\ y(x)=(1)/(4)x+b\rightarrow-3=(1)/(4)(-5)+b\rightarrow b=-3+(5)/(4)=-(7)/(4) \\ \\ \therefore\rightarrow \\ \\ y(x)=(1)/(4)x-(7)/(4) \end{gathered}`

Therefore the perpendicular bisector is as follows:

`\begin{gathered} \text{ Perpendicular bisector:} \\ \\ y(x)=(1)/(4)x-(7)/(4)\rightarrow y(x)=-4x+b \\ \\ \text{ Point of Bisection: }\Rightarrow(x,y)=(-1,-2) \\ \\ \therefore\rightarrow \\ \\ -2=-4(-1)=b\rightarrow b=-2-4=-6 \\ \\ \text{ Finaly the answer is:} \\ \\ y(x)=-4x-6 \end{gathered}`

Plot confirmation: