Mathematics: 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

Step-by-step explanation:6b+6y8u...

Given that a ( 5, 4), b(-3, -2 ) and c(1, -8) are - id5432183030970, zahradawkins2007

jescanarias22

06.01.2022

The slope of the altitude BM is $\frac{1}{3}$

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

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ ---- eqn 1

Given that points of A(5,4) and C(1,-8)

Here we get $y_{2}=-8$

$y_{1}=4$

$x_{2}=1$

$x_{1}=5$

Now substituting the values in eqn (1), we get

$\text { Slope of } \mathrm{AC}=\frac{-8-4}{1-5}$

$=\frac{-12}{-4}$

= 3

The slope of the Altitude BM is given by the reciprocal of the slope of AC since M is the midpoint of AC.

$\text { Slope of } \mathrm{BM}=\frac{1}{\text { slope of } A C}$

Slope of BM = $\frac{1}{3}$

Thus the slope of the altitude BM is $\frac{1}{3}$

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