The points $A(a, 1), B(9,0)$ and $C(-3,4)$ lie on a straight line. The value of $a$ is
(A) 3
(B) $\frac{8}{3}$
(C) $\frac{7}{2}$
(D) 6
(E) $\frac{5}{2}$
Solution 1

To get from point $B$ to point $C$, we go to the left 12 units and up 4 . Therefore, for each unit up, we have gone 3 to the left.

To get from $B$ to $A$, we must go up 1 , and since $A$ is on $B C$, then we must have gone 3 to the left from 9 , ie. $a=9-3=6$.

## Solution 2

Since the three points lie on the same line then

Slope of $A B=$ Slope of $B C$

$$
\begin{aligned}
\frac{1-0}{a-9} & =\frac{0-4}{9-(-3)} \\
\frac{1}{a-9} & =\frac{-4}{12} \\
12 & =-4 a+36 \\
4 a & =24 \\
a & =6
\end{aligned}
$$

ANSWER: (D)

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