How do you find the distance from the point to the line given the equation and the coordinates?
4x-2y-6=0 (1,1)
put the line in slope intercept form
y=mx+b
then,you know the slope of the perpendicular line is the negative reciprocal of m (new slope of perpendicular line=-1/m
So for the perpendicular line...
y=-1/m x + b
put in the point 1,1
1=-/m + b you know m, solve for b.
there is a little formula for this question:
for Ax + By + C = 0
the distance from a point (p,q) to that line is
│Ap + Bq + C│/√(a^2+b^2)
so distance = │4-2-6│/√(16+4)
= 4/√20
= 4√20 /20
= 4√5/5
To find the distance from a point to a line, you can use the formula for the distance between a point and a line. Here are the steps to find the distance between a point and a line:
1. Given the equation of the line, which is in the form of Ax + By + C = 0, where A, B, and C are constants, we can rearrange it to the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the equation 4x - 2y - 6 = 0 can be rearranged to get -2y = -4x + 6 and then y = 2x - 3.
2. Calculate the slope of the line. Since the equation of the line is already in slope-intercept form, we can directly determine the slope. The slope, in this case, is 2.
3. Identify the coordinates of the given point. In this case, the coordinates of the point are (1,1).
4. Use the formula for the distance between a point and a line. The formula is given as:
Distance = |Ax + By + C| / √(A^2 + B^2)
Plugging in the values A = 4, B = -2, C = -6, and the coordinates of the point (x, y) = (1, 1), we get:
Distance = |4(1) - 2(1) - 6| / √(4^2 + (-2)^2)
5. Simplify the equation. Plugging in the values, we have:
Distance = |4 - 2 - 6| / √(16 + 4)
= |-4| / √20
= 4 / 2√5
= 2 / √5
Therefore, the distance from the point (1,1) to the line 4x - 2y - 6 = 0 is 2 / √5, which is approximately 0.8954.