A second line L2 is perpendicular to L1 at R . Find the equation of L2 in the form y=mx+c. Where m and c are constants
Since line L2 is perpendicular to line L1, the slope of L2 is the negative reciprocal of the slope of L1.
Let's say the equation of L1 is y = m1x + c1. The slope of L1 is m1.
So, the slope of L2, m2, is given by m2 = -1/m1.
To find the equation of L2, we need the slope and a point on the line. We know that L2 is perpendicular to L1 at point R.
Let's say the coordinates of point R are (xR, yR).
Using the point-slope form of a line, the equation of L2 can be written as:
y - yR = m2(x - xR)
Substituting the value of m2, we get:
y - yR = (-1/m1)(x - xR)
Rearranging the equation, we get:
y = (-1/m1)x + (xR/m1) + yR
Comparing this equation with the standard form y = mx + c, we get:
m = -1/m1
c = (xR/m1) + yR
So, the equation of L2 in the form y = mx + c is:
y = (-1/m1)x + (xR/m1) + yR, where m = -1/m1 and c = (xR/m1) + yR.