ok, we need to draw both segment of lines... that are parallel.
We need to re draw, because we need more space for point C (-5,16)
The steps to solve this problem are:
1) We draw segment line CD... later,
2) we express the segment line AB,
3) We find the slopes of both segments
4) finally, we found the value of y.
Do you understand? or have questions of the process?
We have done the segment line CD, after that from the graphic we can make a prediction of the value of y, because we need to find a line perpendicular to cd.. like this one (green in the graphic)... line green will be perpendicular to line yellow...
Now, we find the general equation of the yellow line.. that's it:
[tex]\begin{gathered} \text{slope = m = }\frac{\text{(y}_2-y_1\text{)}}{(x_2-x_1)};\text{ C(x}_1,y_1)=C(-5,16);\text{ D(x}_2,y_2\text{)}=D(-8,11) \\ \text{ m = }\frac{\text{(y}_2-y_1\text{)}}{(x_2-x_1)}=\frac{\text{(11}-16\text{)}}{(-8-(-5))}=\frac{\text{(11}-16\text{)}}{(-8+5)}=\frac{-5}{-3}=\frac{5}{3} \\ m=\frac{5}{3} \end{gathered}[/tex]After that, we should remember that two lines are paralell when a multiplication of its slopes it's equal to -1, like this:
[tex]\begin{gathered} \text{slope 1 }\cdot\text{ slope 2 = -1} \\ m_1\cdot m_2=-1 \\ \frac{5}{3}.m_2=-1 \\ m_2=\frac{-3}{5} \end{gathered}[/tex]Finally, we find the generall equation of the line green with the point A(9,2) and the value of its slope m2, we apply:
[tex]\begin{gathered} (y-y_1)=m(x-x_1);\text{ A(x}_1,y_1)=A(9,2);\text{ m=}\frac{-3}{5};\text{ We replace and get} \\ y-2=\frac{-3}{5}(x-9) \\ y=\frac{-3}{5}x+\frac{3}{5}\cdot\frac{9}{1}+2 \\ y=\frac{-3}{5}x+\frac{27}{5}+2 \\ y=\frac{-3}{5}x+\frac{37}{5} \end{gathered}[/tex]Now, to find the value of y in the poin B, we replace the value of x = -1 in the equation of the green line, like this:
[tex]\begin{gathered} y=\frac{-3}{5}x+\frac{37}{5};\text{ x=-1} \\ y=\frac{-3}{5}(-1)+\frac{37}{5} \\ y=\frac{3}{5}+\frac{37}{5}=\frac{40}{5}=8 \end{gathered}[/tex]The answer has the value of 8. In graphic is similar.. green line... It's not equal because I do the graphic at inexact way.
