The line joining the points $A (- 2, 3)$ and $B (a, 5)$ is parallel to the line joining the points $C (0, 5)$ and $D (- 2, 1)$ . Find the value of $a$

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Solution

Given, $A (- 2, 3)$ and $B (a, 5)$
Slope of line joining $A B = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{5 - 3}{a + 2} = \frac{a}{a + 2} (= m_{1})$
Also given, $C (0, 5), D (- 2, 1)$
Slope of line joining $C D = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{1 - 5}{- 2 - 0} = 2 (= m_{2})$
The lines $A B$ and $C D$ are parallel $m_{1} = m_{2}$
$\Rightarrow \frac{2}{a + 2} = 2 \Rightarrow \frac{1}{a + 2} = 1$
$\Rightarrow a = 2 = 1$
$\Rightarrow a = - 1$

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The line joining the points A(−2,3) and B(a,5) is parallel to the line joining the points C(0,5) and D(−2,1). Find the value of a

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The line joining the points $A (- 2, 3)$ and $B (a, 5)$ is parallel to the line joining the points $C (0, 5)$ and $D (- 2, 1)$ . Find the value of $a$