Problema Solution
Find the distance from (-6,6) to the line defined by y=2x+3. Express as a radical or a number rounded to the nearest hundredth.
Answer provided by our tutors
If the line in is given by the equation ax + by + c = 0, where a, b and c are real constants with a and b not both zero, the distance from the line to a point (x0,y0) is:
d = |ax0+by0+c|/(a^2 + b^2)^0.5
In our case y = 2x + 3 can be written as 2x - y + 3 = 0 thus a = 2, b = -1, c = 3
The point is (-6, 6) thus x0 =-6, y0 = 6
d = |2*(-6) + (-1)*6 + 3|/(2^2 + (-1)^2)^0.5
........
........
d = 6.71
The distance is 6.71.