Given the line 4x - 3y = 12, what is the distance between it and the origin
Is it 2.4?
You are correct.
Which method did u use?
I don't know if there is a faster way of doing it then what I'm doing
To find the distance between the line and the origin, you need to find the perpendicular distance from the origin to the line.
First, let's rearrange the equation of the line to the slope-intercept form (y = mx + b):
4x - 3y = 12
-3y = -4x + 12
y = (4/3)x - 4
Now, we know that any line perpendicular to a given line will have a slope that is the negative reciprocal of the given line's slope. The equation of the line perpendicular to this line will have a slope of -3/4.
So, we have a point (0, 0) which lies on the origin and a line with slope -3/4 passing through it. We can use the formula for the distance between a point and a line to find the distance from the origin to this line.
The formula to calculate the distance between a point (x₁, y₁) and a line with equation Ax + By + C = 0 is given by:
d = |Ax₁ + By₁ + C| / sqrt(A² + B²)
In our case, the line has the equation 4x - 3y = 12. So the values of A, B, and C are 4, -3, and -12, respectively. The point (x₁, y₁) is (0, 0).
Plugging these values into the formula, we get:
d = |4(0) - 3(0) - 12| / sqrt(4² + (-3)²)
= |-12| / sqrt(16 + 9)
= 12 / sqrt(25)
= 12 / 5
= 2.4
Therefore, the distance between the given line 4x - 3y = 12 and the origin is indeed 2.4 units.