Answer:
[tex]\displaystyle y=-\frac{4}{13}x+\frac{2}{13}[/tex]
Step-by-step explanation:
Median of a Triangle
The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.
We have a triangle formed by the points A(-9,-4), B(-3.8), and C(7.-2).
The median from vertex C must pass through the midpoint of the segment AB. First, find that midpoint:
The midpoint (xm,ym) is calculated as follows:
[tex]\displaystyle x_m=\frac{x_1+x_2}{2}=\frac{-3-9}{2}=-6[/tex]
[tex]\displaystyle y_m=\frac{-4+8}{2}=2[/tex]
Midpoint AB=(-6,2). This point and C(7,-2) form the required median.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]\displaystyle y-2=\frac{-2-2}{7+6}(x+6)[/tex]
[tex]\displaystyle y-2=-\frac{-4}{13}(x+6)[/tex]
Operating:
[tex]\displaystyle y-2=-\frac{4}{13}.x-\frac{4}{13}.6[/tex]
[tex]\displaystyle y=-\frac{4}{13}.x-\frac{24}{13}+2[/tex]
[tex]\mathbf{\displaystyle y=-\frac{-4}{13}x+\frac{2}{13}}[/tex]
