Given that triangle has points, and , point can be moved along a certain line with points and remaining stationary, and the area of Δ will not change. What is the slope of that line?

(It says the answer in my book which is )

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- Mar 29th 2010, 01:45 AMdannycfinding slope
Given that triangle has points, and , point can be moved along a certain line with points and remaining stationary, and the area of Δ will not change. What is the slope of that line?

(It says the answer in my book which is ) - Mar 29th 2010, 01:51 AMpickslides
- Mar 29th 2010, 02:00 AMdannyc
Yep--it comes out to the right slope. But what's the logic behind it? (Why is the correct line parallel, is there a mini proof or is it more common knowledge that I somehow missed?)

- Mar 29th 2010, 02:05 AMpickslides
Area of a rectangle is always

The base and height will only always be the same (so the area is constant) for C, if C itself is only moving parallel to the line AB.

Draw a picture of ABC and move C around parallel to AB, you will see the base and height are always the same. - Mar 29th 2010, 02:48 AMHallsofIvy
The area of a

**triangle**, of course.

Quote:

The base and height will only always be the same (so the area is constant) for C, if C itself is only moving parallel to the line AB.

Draw a picture of ABC and move C around parallel to AB, you will see the base and height are always the same.