Question

Find the equation of the perpendicular to the line segment joining (4, 3) and (– 1 1) if it cuts off an intercept – 3 from y – axis.

Answer 1

Given, A line segment joining (4, 3) and (– 1, 1) if it cuts off an intercept – 3 from y–axis. 

To Find: The equation of that line. 

Formula used: The equation of line is y = mx + C 

Explanation: Here, The required equation of line is y = mx + c 

Now, c = – 3 (Given) 

Let m be slope of given line = – 1 

Slope of line joining (x₁ – x₂) and (y₁ – y₂) ,m = \(\frac{y_2-y_1}{x_2-x_1}\) 

So, Slope of line joining (4, 3) and (– 1, 1) , m = \(\frac{1-3}{-1-4}\) = \(\frac{-2}{-5}\)

Therefore, m = \(-\frac{2}{5}\) 

Now, The equation of the line is y = mx + c

y = -\(\frac{2}{5}x-3\) 

y + 3 = \(-\frac{5x}{2}\) 

2y + 5x + 6 = 0 

Hence, The equation of line is 2y + 5x + 6 = 0.