Explanation:
The slope of the altitude drawn to side DN is the reciprocal and opposite to the slope of side DN, because the altitude is perpendicular to the side.
First we have to find the slope of side DN. The formula for the slope of a line with points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]
In this problem the points are D(-6, -1) and N(-3, 10). The slope of side DN is:
[tex]m_{DN}=\frac{-1-10}{-6-(-3)}=\frac{-11}{-6+3}=\frac{-11}{-3}=\frac{11}{3}[/tex]
Therefore the slope of the altitude is:
[tex]m_{\text{altitude}}=-\frac{1}{m_{DN}}=-\frac{1}{\frac{11}{3}}=-\frac{3}{11}[/tex]
Answer:
The slope of the altitude is -3/11
