Respuesta :
The rule of the slope of a line has 2 points is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]A = (1, -2), B = (3, 4), C = (-2, 6)
We will take the altitude from A to the opposite side of BC
Then we will find the slope of BC first
x1 = 3 and y1 = 4. point B
x2 = -2 and y2 = 6. point C
We will substitute them in the rule above
[tex]\begin{gathered} m=\frac{6-4}{-2-3}=\frac{2}{-5} \\ m=-\frac{2}{5} \end{gathered}[/tex]The slope of BC = -2/5
Since the product of the slopes of the perpendicular line is -1, then if the slope of one is m, then the slope of the other will be -1/m, we reciprocal it and change its sign, then the slope of the altitude of BC should be 5/2
[tex]m_{\perp}=\frac{5}{2}[/tex]The form of the equation in point-slope is
y - y1 = m(x - x1)
m = 5/2
Since point A is lying on the altitude from A to BC, then
x1 = 1 and y1 = -2 point A
Substitute m and coordinates of point A in the form of the equation above
y - (-2) = 5/2 (x - 1)
[tex]y+2=\frac{5}{2}(x-1)[/tex]The equation of the altitude from A to BC is
y + 2 = 5/2 (x - 1)
