Question

Let point P represent the intersection point of the height, KP, and the base LM. Determine the coordinates of point P

Answer 1

Consider the image:

Notice that the line KP will be perpendicular to the line LM

The slope of LM is:

`\begin{gathered} m=(8-2)/(3-(-2)) \\ m=(6)/(5) \end{gathered}`

since the line KP is perpendicular to line LM then the slope of LM is:

`\begin{gathered} n=-(1)/((6)/(5)) \\ m=-(5)/(6) \end{gathered}`

Since line KP passes through the point K(3,3) then the equation is:

`\begin{gathered} y-3=-(5)/(6)(x-3) \\ y=-(5)/(6)x+(11)/(2) \end{gathered}`

Similarly the the equation of line LM is:

`\begin{gathered} y-8=(6)/(5)(x-3) \\ y=(6)/(5)x+(22)/(5) \end{gathered}`

Therefore the coordinates of P is:

`(0.541,5.049)`