Posted by **jigna** on Sunday, February 25, 2007 at 6:45am.

Find and write down a proof that the product of the gradients of two perpendicular lines is -1

Use trigonometry.

Let the slope of a line from A to B be m1. Let the slope of a perpendicular line from A to C be m2. The tangent (or slope) of the line between these two lines is:

tan (a - b) = (m1 + m2)/(1 - m1 m2)

a and b are the ANGLES of the two lines, measured from the x axis.

(This is a trigonometric identity)

Now IF m1 m2 = -1, then

tan (a-b) = (m1 - 1/m1)/0 = infinity

therefore the angle between the two lines is 90 degrees.

## Answer This Question

## Related Questions

- Geometry - Prove that the tangents to a circle at the endpoints of a diameter ...
- geometry - find the slope of a line that passes through the following points. (4...
- Geometry HELP - Using coordinate geometry to prove that the diagonals of a ...
- Geometry - Write a paragraph proof of this theorem: In a plane, if two lines ...
- algebra 1 - he slope of a line is negative two-thirds. What is the slope of a ...
- Writing this equation - how do I write the equation of a line perpendicular to ...
- Geometry - How do I write an equation of a line perpendicular to the graph of -...
- MATH - For the floor plans given in exercise27, determine whether the side ...
- math - How do I write one equations in slope-intercept form, and three other ...
- algebra - Find the slope of any line perpendicular to the line through points (0...

More Related Questions