Find the equation of lines through origin ,perpendicular to the lines
The equation of a line that passes through the origin can be expressed in the form y = mx, where m is the slope of the line.
To find a line perpendicular to this line, we need to find the negative reciprocal of the slope of the original line. Let's call this new slope m'.
For two lines to be perpendicular, the product of their slopes must be -1. Therefore, m * m' = -1.
Now we can substitute the slope of the original line, m, into the equation:
m * m' = -1
This equation allows us to solve for m'.
For example, let's say the slope of the original line is 2. We can substitute this into the equation and solve for m':
2 * m' = -1
m' = -1/2
So the slope of the line perpendicular to y = 2x is -1/2.
Now we can write the equation of the line perpendicular to y = 2x that passes through the origin:
y = -1/2x
To find the equation of lines through the origin that are perpendicular to a given line, you'll need to follow these steps:
Step 1: Find the slope of the given line. Let's call this slope "m".
Step 2: Perpendicular lines have negative reciprocal slopes. So, the slope of the line perpendicular to the given line would be -1/m.
Step 3: The equation of a line with slope "m" passing through the origin (0,0) can be expressed as y = mx.
Step 4: Substitute the negative reciprocal slope (-1/m) into the equation obtained in Step 3 to find the equation of the line perpendicular to the given line passing through the origin.
So, the equation of lines through the origin perpendicular to the given line is y = -1/m*x.