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

Let Point P Represent The Intersection Point Of The Height KP And The Base LM Determine The Coordinates Of Point P class=

Sagot :

SOLUTION

Consider the image:

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

The slope of LM is:

[tex]\begin{gathered} m=\frac{8-2}{3-(-2)} \\ m=\frac{6}{5} \end{gathered}[/tex]

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

[tex]\begin{gathered} n=-\frac{1}{\frac{6}{5}} \\ m=-\frac{5}{6} \end{gathered}[/tex]

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

[tex]\begin{gathered} y-3=-\frac{5}{6}(x-3) \\ y=-\frac{5}{6}x+\frac{11}{2} \end{gathered}[/tex]

Similarly the the equation of line LM is:

[tex]\begin{gathered} y-8=\frac{6}{5}(x-3) \\ y=\frac{6}{5}x+\frac{22}{5} \end{gathered}[/tex]

Therefore the coordinates of P is:

[tex](0.541,5.049)[/tex]

View image LarsonL517949
View image LarsonL517949
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