A line passing through the points (a, 2a) and (-2,3) is perpendicular to the line 4x+3y+5=0, find the value of a.

\frac{17}{6}

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\frac{18}{5}

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\frac{14}{3}

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None of these

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Solution

The correct option is A $\frac{18}{5}$
Let $m_{1}$ be the slope of the line joining A(a, 2a) and B(-2,3). Then, $m_{1} = \frac{2 a - 3}{a + 2}$

Let $m_{2}$ be the slope of the line $4 x + 3 y + 5 = 0$ . Then, $m_{2} = - \frac{4}{3}$

Since given lines are perpendicular. Therefore,
$m_{1} m_{2} = - 1$
$\frac{2 a - 3}{a + 2} \times - \frac{4}{3} = - 1$

$8 a - 12 = 3 a + 6$
$a = \frac{18}{5}$

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Similar questions

(2, 3)

4 x - 3 y = 10

Find the equation of the line passing through the points (2, 3) and the point of intersection of the lines $4 x - 3 y = 7$ and $3 x + 4 y + 1 = 0$ .

(2, 3)

4 x - 3 y = 10

x + 2 y = 5

3 x + 7 y = 17

3 x + 4 y = 14

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