find the distance between these two point
(3,4) and 2x-y=0
show step
Your wording is incorrect.
Did you mean :
find the distance from the point to the given line?
yes sir reiny
There are several ways to do this:
1. There is an actual formula to do this, Google
"distance from a point to a line" and study it
2. rigorous method. There is a great video form the KhanAcademy webpage that explains in great detail . Your line is y = 2x , (easier than theirs) and your point is (3,4)
https://www.khanacademy.org/math/geometry-home/analytic-geometry-topic/distance-between-a-point-and-a-line/v/distance-between-a-point-and-a-line
let me know what you got.
To find the distance between the point (3, 4) and the line 2x - y = 0, we can use the formula for the distance between a point and a line.
The formula is:
distance = |Ax + By + C| / sqrt(A^2 + B^2),
where (x, y) is the point and (A, B, C) are the coefficients of the line equation.
Let's begin by rewriting the line equation in the form Ax + By + C = 0:
2x - y = 0
-2x + y - 0 = 0
So, A = -2, B = 1, and C = 0.
Now, substitute the coordinates of the point (3, 4) into the formula:
distance = |-2(3) + 1(4) + 0| / sqrt((-2)^2 + 1^2)
distance = |-6 + 4| / sqrt(4 + 1)
distance = |-2| / sqrt(5)
distance = 2 / sqrt(5)
Therefore, the distance between the point (3, 4) and the line 2x - y = 0 is 2 / sqrt(5).