The points $$ (-4,-5),(a,-2) $$ and $$ (6,1) $$ all lie on the same line. The value of a i $$ \begin{array}{lll} ext { A } 0 & ext { B } 1 \ ext { D }-1 & ext { E }-2\end{array} $$

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The points $$ (-4,-5),(a,-2) $$ and $$ (6,1) $$ all lie on the same line. The value of a i $$ \begin{array}{lll}	ext { A } 0 & 	ext { B } 1 \ 	ext { D }-1 & 	ext { E }-2\end{array} $$

UpStudy AI · Accepted Answer

Let the points be $$ A(-4,-5) $$, $$ B(a,-2) $$, and $$ C(6,1) $$. Since the points are collinear, the slope between $$ A $$ and $$ B $$ must equal the slope between $$ A $$ and $$ C $$.

1. Compute the slope between $$ A $$ and $$ C $$:
   $$
   m_{AC} = \frac{1 - (-5)}{6 - (-4)} = \frac{6}{10} = \frac{3}{5}.
   $$

2. Compute the slope between $$ A $$ and $$ B $$:
   $$
   m_{AB} = \frac{-2 - (-5)}{a - (-4)} = \frac{3}{a+4}.
   $$

3. Set the slopes equal:
   $$
   \frac{3}{a+4} = \frac{3}{5}.
   $$

4. Cross multiply:
   $$
   3 \times 5 = 3 \times (a+4).
   $$

5. Simplify and solve for $$ a $$:
   $$
   15 = 3a + 12 \quad \Longrightarrow \quad 3 = 3a \quad \Longrightarrow \quad a = 1.
   $$

Thus, the value of $$ a $$ is $$1$$.
The value of $$ a $$ is $$1$$.

The points and all lie on the same line. The value of a i

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