Find the equation of a line which is perpendicular to the line joining (4, 2) and (3 5) and cuts off an intercept of length 3 on y – axis.

Question

Philoid · Accepted Answer

Given, A line segment joining (4, 2) and (3, 5) 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₎ ,

So, Slope of line joining (4, 2) and (3, 5),

Therefore,

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

x – 3y + 9 = 0

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