Find the distance from the origin to the line x-2y=4
for the point (p,q),
the distance to the line Ax + By + C = 0 is
|Ap + Bq + C|/√(A^2 + B^2)
so .....
To find the distance from the origin to a line, we can use the formula for the distance between a point and a line. In this case, the origin is represented by the point (0, 0), and the line is represented by the equation x - 2y = 4.
Step 1: Rearrange the equation
First, let's rearrange the equation in the form y = mx + b, where m is the slope and b is the y-intercept:
x - 2y = 4
-2y = -x + 4
y = (1/2)x - 2
Step 2: Find the perpendicular distance
The distance between a point (x0, y0) and a line Ax + By + C = 0 can be found using the formula:
Distance = |Ax0 + By0 + C| / √(A^2 + B^2)
In our case, A = 1, B = -2, and C = -4 (obtained by rearranging the equation in the form Ax + By + C = 0). We need to find the distance from the origin (0, 0), so x0 = 0 and y0 = 0.
Substituting these values into the formula, we get:
Distance = |1(0) + (-2)(0) + (-4)| / √(1^2 + (-2)^2)
= 4 / √(1 + 4)
= 4 / √5
Therefore, the distance from the origin to the line x - 2y = 4 is 4 / √5.