Given that A ( 5, 4), B(-3, -2 ) and C(1, -8) are the vertices of a triangle ABC, find the slope of altitude BM

Answer: The slope of the altitude BM is [tex]\frac{1}{3}[/tex]Solution: Given that A(5,4), B(-3,-2) and C(1,-8) are the vertices of a triangle ABC . We have to find the slope of altitude BM The figure of the given question is given below. Here M is the mid-point of side AC. To find the slope of altitude BM, we need to first find the slope of AC. The slope of AC is given by [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]  ---- eqn 1 Given that points of A(5,4) and C(1,-8) Here we get [tex]y_{2}=-8[/tex][tex]y_{1}=4[/tex][tex]x_{2}=1[/tex][tex]x_{1}=5[/tex]Now substituting the values in eqn (1), we get [tex]\text { Slope of } \mathrm{AC}=\frac{-8-4}{1-5}[/tex][tex]=\frac{-12}{-4}[/tex]= 3 The slope of the Altitude BM is given by the reciprocal of the slope of AC since M is the midpoint of AC. [tex]\text { Slope of } \mathrm{BM}=\frac{1}{\text { slope of } A C}[/tex]Slope of BM = [tex]\frac{1}{3}[/tex]Thus the slope of the altitude BM is [tex]\frac{1}{3}[/tex]