First slide

Equation of line in Straight lines

Question

If a,b are intercepts of the line which is perpendicular to the line passing through the points $(3, 5), (4, 3)$ and passing through the point $(5, 6)$ then $\frac{a}{b} =$

Easy

A

-2
B

-3
C

-1
D

-5

Solution

The slope of the line joining the points $(3, 5), (4, 3)$ is $m = \frac{3 - 5}{4 - 3} = - 2$
Equation of line passing through the point $(5, 6)$ and perpendicular to the line having slope -2 is
$\begin{matrix} y - 6 = \frac{1}{2} (x - 5) \\ 2 y - 12 = x - 5 \\ x - 2 y + 7 = 0 \end{matrix}$
Isolate the constant term and then divide with that constant on both sides
$\begin{matrix} x - 2 y = - 7 \\ \frac{x}{- 7} + \frac{y}{\frac{7}{2}} = 1 \end{matrix}$
Therefore, $x - intercept$ is $a = - 7$ and the $y - intercept$ is $b = \frac{7}{2}$
Hence, $\frac{a}{b} = - 2$

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