Given the intercepts of a straight line on both the axes as m and n. The task is to find the length of the normal on this straight line from the origin.
Input: m = 5, n = 3
Input: m = 13, n = 9
Approach: A normal to a line is a line segment drawn from a point perpendicular to the given line.
Let p be the length of the normal drawn from the origin to a line, which subtends an angle Θ with the positive direction of x-axis as follows.
Then, we have cos Θ = p / m and sin Θ = p / n
Since, sin2 Θ + cos2 Θ = 1
So, (p / m)2 + (p / n)2 = 1
We get, p = m * n / √(m2 + n2)
Below is the implementation of the above approach:
# Python3 implementation of the approach
# Function to find the normal
# of the straight line
def normal(m, n):
# Length of the normal
N = ((abs(m) * abs(n)) /
math.sqrt((abs(m) * abs(m)) +
(abs(n) * abs(n))));
# Driver code
m = -5; n = 3;
# This code is contributed
# by Akanksha Rai
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