In the diagram, $D$ is the point on $B C$ so that $A D$ is perpendicular to $B C$. The slope of $A D$ is
(A) $\frac{3}{11}$
(B) 1
(C) $-\frac{15}{11}$
(D) $\frac{2}{7}$
(E) $\frac{2}{5}$

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-123.jpg?height=439&width=390&top_left_y=331&top_left_x=1320)
From the diagram, we see that the line segment $A D$ is perpendicular to the line segment $B C$, and so the product of the slopes of these two line segments is -1 .

The slope of segment $B C$ is $\frac{7-(-4)}{6-9}=-\frac{11}{3}$, and so the slope of $A D$ is $\frac{3}{11}$.

(We notice that we did not use the coordinates of $A$ !)

ANSWER: (A)